I kind of agree with Swiftcoder. Skin them any way you like, give them any name you like, but what you've described will still feel like zombies to people. L4D and Resident Evil may call their creatures zombies, but their basically just human mutations with a nasty rage problem. In L4D they actually are the walking dead, but in some of the RE games the zombies aren't corpses at all (Majini from RE5). Even Dead Space felt like a bit of a zombie shoot 'em up to a certain extent.
My real question is; are people really sick of zombie games? I think maybe they're sick of bad zombie games (since there are so many), but I don't think the genre is losing fans.
If you really want to avoid the zombie genre consider removing some of the basic requirements for your creatures.
"Driven by base instincts"--This can easily apply to most zombie critters, but also to numerous other things. How bout a behavioral pattern of some sort? Maybe a learning curve as the game progresses (Think Jurassic Park--the raptors learn to open doors, OMG WE'RE SCREWED!!!). I know this learning curve happens in some zombie games, but usually in a drastic way (zombies go from claws to rocket launchers in one level). It's always a bit unnerving when you're playing a horror game, you see the bad thing, it sees you, you ready to shoot it down as it inevitably charges right at you like all the rest... and suddenly it runs away. Consider a zombie ambush that actually feels like it was set up by the zombies and not the game designers (I Am Legend vs L4D Zombie Rushes)
Practically Blind--Is a pretty standard zombie feature, that's why the swarm is always following the protagonist. I'm a fan of this trope, but it's another thing you may want to discard if you want to avoid the zombie genre. It does make for some awesome storyline (High School of the Dead does some amazing things with blind zombies).
Drawn to Life--Definitely drop if you want to avoid the zombie genre... why not give your nasties a modicum of intelligence and give them a reason for wanting to kill anyone unlike them. "Mutant good! Normie bad!" Is the simplest level, but also consider what it would be like if your creatures were of a hive mind of some sort.
Nocturnal--Again... very typical zombie trope. They always move in larger groups at night.
Can only be killed by 'Removing the Head or Destroying the Brain'--I quoted Sean of the Dead if you didn't notice... probably enough said on this factor.
Infectious--It's very rare to find a zombie game that doesn't feature this.
Either just go with what you've got (it looks great and sounds interesting so far), or you'll really need to make some drastic changes to your game to avoid it being a zombie type game, which in my opinion is totally fine. I'm not sure where you heard that zombies were losing popularity. Walking Dead, Resident Evil, Day Z and many other zombie things are still insanely popular.
Or are you more worried that you're game will simply get lost in the ocean?
I think the concept is pretty interesting, and my idea sort of jumps back to every one who said "make the bad guy bad enough and there's your reason". Expanding on that, it's pretty easy for one person with a modicum of power to somehow influence the lives of just 15 people, giving them a reason to all hate the final boss. The interplay between your characters can be as elaborate or as simple as you desire it. Soul Calibur comes to mind for me, as there is an immense amount of interplay between all of the characters--they all want to kill the same big bad boss, but all for slightly different reasons. Now, to show my age, Streets of Rage or Final Fight also come to mind as the opposite extreme. The bad boss is bad, the main characters are good (until the third SoR, when things get complicated just a little bit). The main characters are just friends for some reason.
Breaking it into the more complex, enthralling story would be a lot more fun in my opinion, and would probably get your audience hooked. Great storylines can turn simplistic games into masterpieces.
What I'd like to know is just who are these characters? I know you're not sure about the details, but what about fighting styles, setting, and gameplay? Will there be firearms? Basic street weapons? Do each of the characters practice some form of Martial Arts (including those that aren't recognized as such)? Is it fantastic or does it maintain a level or realism (is everybody hurling balls of fire at each other, deflecting bullets with swords, ripping apart robotic henchmen)?
Since you already have a game in design I'm guessing you have some of these elements cemented in.
Still, here's my suggestion.
1-Gilgamesh: The Big Bad Boss. Leader of the Tower of Babel, the nastiest gang in the city. Until the arrival of Babel the various criminal organizations in the city warred for control. Gilgamesh is a small but ruthless man, a student of Legend, War, and the Martial Arts. No matter the odds he always emerges unscathed from his battles, leaving a trail of broken bodies. Gilgamesh seized power by ruthlessly hunting down and killing anyone with any ties to the opposing gangs, forcing many people to flee the city or to go deep into hiding. People have begun to wonder whether or not he is actually the king of legend.
2-Enkidu: The Big Bad Boss' Buddy (henchmen, but I'm having fun with alliteration here). Gilgamesh's burly right hand. Enkidu fights with the ferocity and power of a rabid bear. His bestial nature goes deeper than his fighting style, however, and the atrocities he has committed stand as testaments to is total lack of human compassion.
3-Ai: The Lioness' Pride. Although Ai is only nineteen she has already mastered the defensive art of Jeet Kune Do. Her talents lead to her well-known pride among martial arts circuits that 'No man can even touch me'. She frequently taunts and ridicules her opponents, and despite her mastery of the form of Jeet Kune Do has utterly failed to retain any of its temperance. Hearing of Gilgamesh's atrocities and prowess in combat has piqued Ai's pride. She sees herself as a noble warrior, and: "Like always, when a man fails to clean up a mess it's time for a woman to show him how it's done."
4-Aito: The Crane's Composure. Very few would guess that Aito is Ai's twin brother. Like his sister he has spent his life in the study of Kung Fu, but he focused instead on the Wing Chun style. Aito has taken to heart the concept that a martial art is meant for more than just conditioning the body. His extreme patience and composure often lead him to be thoroughly overshadowed by his sister's overbearing nature: few would say they have ever even heard him speak. "Pride may often come before the fall, but the fall's not so bad if someone is there to catch." Aito's only reason to seek out Gilgamesh is to protect his sister, an idea he would never mention to her. Note: Aito and Ai's interaction/characters will change depending on whether or not they are played together.
5-David: Hand of Death. Lots of people want to see Gilgamesh dead, and some of them have the resources and knowledge to try and do something about it. On the surface David is extremely polite and humble, but beneath he is usually something much more sinister. Anyone who has any dealings with the underground has heard his true name, the Hand of Death. David has been hired by the few remaining crime-lords to put an end to Gilgamesh, and he has been promised a bonus for any of Gilgamesh's underlings he hurts/kills along the way. Practiced in various martial arts forms, David prefers Krav Maga to disable or kill his opponent, but isn't beyond using whatever weapons he can find at hand. He uses his charming nature in preference to stealth to set his opponents at ease. David is not the original Hand of Death, but actually the third, and he carries that legacy proudly.
6-Mali Mali: The Exile. Mali Mali was originally taught Muay Thai by her father as a means of self-defense. Although he was an expert of Muay Thai her father barely lasted a minute when Enkidu came to their home. She was forced to watch as her father fought for his life against the savage beast. When he was finished dismembering her father Enkidu did something surprising, he relented in his slaughter. He muttered one word to Mali, "Exile", before leaving her home. His shocking display of mercy did not go unnoticed by Mali, and she began to believe that Enkidu was somehow mislead or enslaved by Gilgamesh--that he was not the wild beast that rumors said. She began to grow concerned for him, and worried that should she remain that he would somehow be punished. She did not forgive the act, however, merely shifted all of her rage onto Gilgamesh. So she took up a mask (full head wrapping with trailing scarfs in my imagination) and took to the streets to find Gilgamesh and exact her revenge. Note: Mali will barely speak at all, especially when paired with other PCs. Any text for her will be curt and sound somewhat irritated with the exception of fighting with Enkidu. For that battle she will suddenly come alive in pleading for mercy on his behalf. Her plea will only affect one character's decision, David's (who has taken an odd turn at Mali's frequent snubs and fallen in love with her), who will choose instead to spare Enkidu on Mali's behalf (endearing him to her at last).
I think I'll stop the detailed descriptions here... This might be too huge a wall of text already. I have ideas to fill in the rest of the characters if you like where this is going, but I think I'll relent for now.