What you really need is human inspiration. I personally believe it's rather impossible for humans to construct truly alien cultures. We just dont have the imagination. Instead we construct human cultural aspects and give them alien form. This way what you really need is to figure out what human cultural aspects inspire your various species.
The issue is I can't make them an expy of a real human culture. They all have to be (and are) unique. They have a particular set of traits that humans may identify with, but also have a set of traits that humans do not have. I cannot cheapen them by basing them off of a real-world culture.
You can convey this by making the aesthetics of the different races resemble human cultures in subtle way. For instance. The slave loving "Simini" could use roman-looking architecture in their buildings or roman-looking combat armor. Or move in phalanx formations or something. If anyone is using a zerg-rush strategy try to sneak in a reference to the D-Day landing in Normandy or something. Game music and quotes and unit greetings can help this along too.
You're mistaking a symptom for the cause. Simini don't love slavery. If any simini was asked what they thought of slavery, they would tell you it is a disgusting and inhumane practice, and they truly believe that. Their actions are a result of their disdain for other species, they think of other species as animals and believe it's alright to enslave them because of that. While they do acknowledge that other species are above common animals to some extent, they don't see enough difference to give them any more rights than an animal.
Think about star craft:This is the cinematic when completing the terran campaign in the original brood war expansion:
Look how closely it resembles the world war 2 propaganda films:
Even down to the music it's clear to see what the inspiration is.
We know. That said, Star Craft is a bad example. The three factions are all planets of hats, bereft of any complexity or variation that might redeem them.
Now think about what makes the Protoss seem noble in your eyes.
It's in their dialogue. The music. The sleek architecture of golden structures. Their tall stature. These are all how you'd make a human look proud and alien at the same time. The fact that their structures are all golden and their home planet is green makes me think of how the aztecs must have seemed to the spanish conquistadors. Alien and honorable at the same time.
Yeah, no. The aztecs didn't seem "honorable" to anybody. The spanish saw them as evil, sub-human monsters to be slaughtered en masse for their profit. (Although I can't argue the "evil" part.)
So my advice to you is to figure out what human cultural aspects inspire each species in your game. Then start making that the template on their cultural design as much as possible.
Alright then, let's try the simini.
The simini are arrogant and self-obsessed and care no more for the lives of other species than Americans care for the lives of whatever "savages" they're bombing at the time. They also have a silly phobia that overwhelms all their senses (mention their ocean anywhere near them, they'll all get uncomfortable) and tend to get tunnel vision when working with one thing for too long. Hm. What human culture does that... oh, right, all of them. That really narrows it down.
Alright, maybe we'll have better luck with the bahaar.
The bahaar are servile, devoted and unquestioningly loyal. They follow the commands of their master to the death, and put down any among their numbers that dissent even slightly. They commit horrid atrocities without a second thought on the word of their masters, never even stopping to think that maybe their master didn't think the order through or might not have meant it quite the way they think. They also think that such unquestioning obedience is a virtue, and that the atrocities they commit are just, just because it's their master's will. Now what culture would... wait, that's any and every military in the history of the world. That doesn't get me anywhere either.
The ferroningen are practical, pragmatic and have no concept of morality outside of practicality. If they say something is "wrong", they mean that at some level it causes problems for them. They don't have any religions, they don't make art, they don't wear clothing, they don't have music. They do have emotions, but those emotions are hidden at all times until they go completely ballistic. They have a lamarckian memory that makes some inherently better suited for particular tasks, and as a result develop into particular tasks very well and do poorly outside of them, creating regimented castes in their very nature that don't seem wrong to them and really aren't. Now what human culture could possibly fit that? None? Huh.
This doesn't appear to be working too well. Maybe it's because these aren't planets of hats, and their cultures are too complex to be covered by referencing a human culture known for a single trait of theirs? It's starting to look that way.
Seriously, this is a bad idea for a cheap writer too lazy to make anything unique. Basing them off a human culture cheapens them, removes any point of complex or developed characters, prevents you from expanding or developing them and dehumanizes both them and the culture in question. It turns them into one big stereotype, and that is good for nothing and nobody. Small cultural references and inspirations are alright, but outright basing them, even just in appearance, off of a real-world culture is stupid. Especially basing them off it "as much as possible."
So how can this be done right? There's definitely a way, because it has been done. Let's go ahead and see this trope done right.
Halo. There we find this done right all over the damn place, but let's look at one examples: Sanghieli.
The sanghieli have inspirations in for the military castes of feudal Japan. They are honour-bound warriors with a respect for their enemies and known to welcome their enemies into their ranks. Their aristocrats, and only their aristocrats, wield swords in battle, and cannot wed but can take any mate they choose. They have a heavy emphasis on honour and skill in battle, are strongly loyal to their kin, believe that death in battle is honourable and have been known to commit ritual suicide to preserve their honour rather than be captured.
What makes it alright to use human cultural references to add to the character of your fictional culture? What makes this constructive, rather than destructive? Moderation. Basing single aspects of them off another culture is fine, but basing them entirely off of one, or "as much as possible", is a problem. Sanghieli have a lot of references to feudal Japan, but they have enough truly unique traits and other influences to make it come across as just a part of what they are instead of everything there is to them. Their appearance is unique and different, their culture has other aspects and their society is structured differently. They don't come off as a walking stereotype like the factions of Starcraft, they are actually alien.
Now let's try some moderation, here. Try drawing from a larger pool and adding unique traits. Thankfully, I've already done this for one faction: the kokome.
Kokome are descendants of humanity, (I know it's weird to say that with a game that takes place in 1985) who have spent decades under simini rule. Finally free of the simini and seeking to create their own culture, they turned to the history of the three locations most of their ancestors they were abducted from: Japan, Germany and Mexico. They also retain many influences from the Simini and the natives of Kakara. Now that the coalition is present, they're gaining ferroningen and andhieli traits as well.
Kokome speak a language called "Katahmah", which comes from a Zolaisn (Kakaran native) word meaning "of all those here", which uses Japanese grammatical structure with Japanese, German, Spanish, Nahuatl (Aztec), Canabi (Simini) and Zolaisn vocabulary. As of the present, they are beginning to incorporate ferroningen and andhieli words. This language varies heavily in vocabularly, slang and syntax depending on region. For instance, on Kakara I ferroningen influence is very strong, so ferroningen contractions are used. These compounds combine the key words in a common phrases together for the sake of brevity, and often extend to as many as six or seven words. Entire sentences become contractions, which serve the same purpose as idioms.
Kokome clothing varies by region, but the most common are imperial uniforms. Their uniform is a simini-style tunic (just short of the knee, sleeves just short of the elbow) without the folded collar, simini-style boots (almost knee high, buckled instead of laced, built to prevent chafing without a sock) designed for human feet and simini-style gloves (almost elbow length, fingerless, small zipper on the inside to ease removal while keeping them secure) designed for human hands. Hole in the back of the tunic for the kokome to fit their tail through, which was not previously present because the Simini amputate their tails. (No reason why. Just like there's no reason why humans remove their foreskins.)
The tunic has a belt around the waist with mounts for other objects, such as scabbards, holsters and satchels. No undergarments, although some kokome wear stockings on the outer planets, and some even go so far as including a full, simini-style jumpsuit underneath. If headgear is worn, they wear a shortened simini headress that only extends down the back of their head and does not cover their neck. (Simini headresses are a cloth attached to a headband, with buttons near the bottom of each side, with holes for the ears. It is draped over the back of the head, with the two sides fastening in the front and the bottom tucked into their collar.) Kokome clothing is strong and protective, usually made of tough materials such as leather or carbon fibre, with softer inner layers to prevent chafing. Regular kokome clothing has been known to halt shrapnel and even small arms fire, which is overkill for its typical purposes.
Kokome formal attire varies by planet. On Kakara I, they wear thin, lightweight robe with a cloak, cowl and face mask. This outfit designates them as imperial nobility, breathes very well in the hot environment and protects them from the sand, and the kokome usually goes nude when formal or protective attire is not required. (It's a practical thing, their planet gets HOT.) On kakara II, they wear an overcoat extending down to the knees, over either more common clothing, a light robe, or nothing. This overcoat is lightweight and cool, and is easily removed to allow for lighter (or no) attire when it is not required. On kakara III, where fashion is a bigger deal, it's hard to pick a most common wear although the clothing they use is all traditional Japanese. The most formal would be a kimono, but otherwise outfits such as a haori and hakama. On kakara IV, full simini-style outfits with a full simini headress underneath a heavy duster are preferred, because that planet is just too cold for light clothing. All of these are generally made of softer, more expensive, but no less protective materials and are designed to be comfortable and practical. All of these are also usually "simini blood" blue.
Kokome armour also varies by region, but the most common light armour is Imperial armour. Imperial armour fits over the top of an imperial uniform, clasping directly to the boots, gauntlets and tunic, and has seperate knee and elbow guards. Their most common medium armour is similar to the medium armour worn by ashigaru and samurai in feudal Japan and is often worn with a simple suji or zunari kabuto, (no mengu) with the next most common being more western-style light plate over chain, in term over fabric. (Plate cuirass, knee and elbow pads, boots and gauntlets, chain underlined with fabric over the rest.) This is worn with a gefechtshelm, also usually metal over fabric. Their most common heavy armour is western-style heavy lamillar armour, with large horizontal bands of metal and plastic, with removable ceramic plates sometimes being fixed to the top. Their helmet there is a heavy, western full-helm with a transparent visor rather than a slotted one and less impractical embellishments than normally found on western mail. The next most common heavy armour is a heavier version of the Japanese medium lamellar made out of metal and plastic bands with removable ceramic plates. These come with an eboshi kabuto and a mengu-style facemask that (unlike an actual mengu) is part of the helmet and has transparent eye pieces and a filter over the mouth instead of holes. All of these historically-insprired armours have modern features, and are often smaller in size, closer to the body and overall more flexible with less embellishment than the armours they evolved from. These fit tightly and are altered to be more practical instead of stylish.
Kokome culture is based heavily around fairness and personal merit, as after decades under simini rule they've learned their lesson about class divides. Their government is meritocratic, they NEVER charge for education, private schools are illegal (there are cyberschools, but those are run by the government) and most children live on their own near their parents, rather than with their parents, and earn their own living. Basic housing, at least somewhat edible food and most health care is provided free, (sometimes there's a co-pay instead to prevent abuse) taxes rise sharply with income (from a low starting point) and there isn't as large of an income gap between positions due to a high minimum wage and low cost of living. While there is still a class divide, it is smaller than in any other capitalistic society in existence, by a HUGE margin. This is intended to help level the playing field and make success be dependent on merit, rather than wealth. There is no support for those with little ability, but there are enough roles in society and enough options throughout education to make up for a weakness (no matter how large) in one area with just an equal strength in another area.
Kokome have no special laws regarding any particular species, subspecies, breed, sex, age or religion, and judge everybody purely by their own personal merit. They also don't allow you to use your species, subspecies, breed, sex, age or religion as an excuse for a lack of merit. If any of these things make you poor at something, you WILL be mocked for your failure regardless. Don't like it? Either figure it out or give up. For them, success is about finding something you have talent with and getting better at it. You will not be successful if you aren't talented at what you want to do. You can make a living doing almost anything if you're good enough at it, no matter what that may be. The kokome themselves are physically and mentally strong, and their distribution of talent is more extreme, meaning that at some things they are phenomenal and at other things they totally suck. (In-game, this means their tag skills and dump skills have more effect.) They tend to be drawn to fields that are demanding physically or mentally, especially those that take a lot of skill. Militarily, they tend towards weapons and vehicles that require a great deal of skill and either physical or mental ability, and usually wear light or medium armour, only rarely heavy armour or clothing.
Now take a second, there ARE a number of real-world inspirations for their culture beyond just the clothing. See if you can spot any of them. No? That's a good thing. Any inspiration should be subtle and moderate. It gives them a much more unique feel, which is something you want in a fictional culture.