You've gotten plenty of information here, from various sources, and most of it is accurate. However, let me give you some practical advice:
Re. Copyright - as discussed by numerous individuals above, a copyright protects the specific expression of a work. In the video game world, two items can generally be protected by copyright: a) the code; b) the performance (so to speak). Think of the performance as the combination of the story, script, setting, actions, characters, etc. Movies can be copyrighted in the same way, and although they don't have interactivity, there are many components that in combination can be protected. The code too can be copyrighted. Should you copyright your game? Yes, it always makes sense to do so. Will copyright protect your combat system? Maybe. Here's the difficulty. The copyright of the code would protect from someone taking your code verbatim and using it again. It would be more difficult however to prove infringement if they used it as reference but created their own system.
Re. Patent - As numerous individuals suggest, a patent of a combat system is probably available. For example, in the game business the ghost car patent protects its owner from infringement. In the same way, theoretically, a patent of your unique combat system would protect you. But here's the difficulty: patents are very expensive to obtain, and astronomically expensive to litigate. To give you an example, most good patent attorneys will tell you that your base line cost (US) to obtain a US patent is in the neighborhood of $50-$80K. Litigation is in the millions. My guess is that unless you have an aunt who is a patent attorney with lots of time on her hands, the patent is out of reach.
Option 3: a well written license, protecting your trade secrets. I won't go into the details here, but if your system is unique and attractive to others, the buy versus build option for them may allow you to exploit your property with a semblance of protection.
And yes, I'm an IP attorney working primarily in the video game and social media industries. That said, this does not constitute legal advice nor does it confer any sort of legal relationship between us. I'm simply adding my two-cents to a general discussion of the differences between IP rights.
In the article I outline the basic idea of what can and can't be copyrighted.
While I am NOT giving you legal advice here, the basic idea of a robotic warrior, as in MechWarrior, as in the television series Falling Skies, as in BattleTech games, as in Sierra/Dynamix's Metaltech video game series, has been repeated in television, movies, and games to the point that a unique unit with similar attributes would probably not infringe the MechWarrior franchise under the scenes a faire doctrine.
That said, as you mention, you DO NOT have the right to copy the specific mechs within the Mechwarrior universe, nor copy their specific attributes, etc.
As I've mentioned in previous posts, this is NOT specific legal advice and the purpose of my response is editorial only, to communicate the basic ideas and concepts of copyright and copyright defenses. Make sure you clear your specific creations with a knowledgeable lawyer before you publish. There's lots of gotchas out there. For example, Treasure Island may be in the public domain, but Disney's Treasure Island film, including the specific deviations they've taken from the original book, are protected.
As Tom suggested earlier, your use is called "copyright infringement" not "fair use". In the context you've described, there's nothing fair about stealing someone's artwork, simply because you haven't been able to contact them.
Under US Copyright law, infringement carries a statutory fine of $750-$30,000 per instance. Where there is willful infringement, at the court's discretion, the award of damages can be as much as $150,000 per work.
What you've described is willful infringement, so as Tom has suggested, "don't do it."
BTW: Please do not consider this legal advice. Your circumstances, etc. may be more complex than what you've described, and the purpose of my response is editorial only.
The issue that you're talking about is one that is not uncommon among many creative endeavors. Unfortunately, as you have sensed, the road that you've begun to go down with your co-collaborators is one plagued with issues and misunderstandings. My common-sense advice is to see if you can retract and find agreement between the parties before creation of assets actually begins.
Here's the basic legal problem that you're facing:
Under US Copyright Law, creative works are, by default, owned by the creators themselves, unless some other arrangement, such as a work-for-hire, employment, etc. trumps that basic assumption. So, let's say that an artist on your team of co-conspirators begins creating the basic characters for the game. You're the programmer, and you begin writing the underlying game code. Both of you intend to contribute to the game in this way, but suddenly the artist finds a better gig, and no longer wants to work on the game.
Question: Do you have any rights to the characters they've created?
Answer: Without a contract of some kind (be it an collaboration agreement, partnership agreement, work for hire agreement) the answer is "it's going to be tough." I hesitate in answering "no" because, without getting into the details, there is a concept called reliance doctrine that may create a bit of leverage. There is also an argument that you've created some ownership in the collective work as co-creators. But the message is that you've greatly muddied the waters, and mue=money, when it comes to asserting ownership on a creative work.
Hopefully, I've not confused you or the issue.
Please note that while I am an attorney working in the video game industry, this is not legal advise, nor should you rely on it in any way in making your legal decisions. Good luck out there.