I had the idea of perhaps a group of four or so banding together and winning the game. I was going to have additional M.A.D or M.E.L.D be rewarded with each death, but with out the elimination requirement the entire group might simply work together, and kill off any of the NPC or Arena threats. This will need to be altered, and I am open to ideas :)
What you need to consider here is that humans will generally band together in the face of danger. Sure, there will be a lone wolf or two, but in a survival situation, such characters would realistically be the first to die. If you want to bring a sense of conflict in the story without outright forcing the characters to kill each other you should bring in a different stake right at the start of the story. Off the top of my head, putting the tournament on a time limit wherein all contestants die if it runs out would be a good way to add tension to the story as a whole. It would drive characters to do reckless things that they would otherwise not even consider just to shave a few hours off of a task. It can also lead to conflict wihin the group as the ever enchroaching end of the time limit drives people to ever more reckless actions, possibly endangering or even leading to the deaths of other characters or themselves.
The supernatural abilities are rolled at random, so someone can't pick what they want. But the limitations would indeed need to be stated along with the power reveal once they have rolled. I was thinking each ability would have a simple statement as how it could be used. Example: You gain the ability to launch a fireball up to 10 feet doing (x) damage, however you take (x) damage of cold due to the exertion. Let me know what you think about that and how it could be tweaked.
Your example uses quite a lot of absolute rules. This can work in a tabletop game, but, speaking from personal experience, this manner of rules mostly works to stifly more freeform manners of roleplaying such as what this seems intended to be. Using this example you would either need hard rules to state how far a character can move in a given 'turn' or else constantly require people to keep track of their exact location. The former brings an even larger rules load with it and the latter just doesn't sound fun at all if you ask me. Hard rules in a freeform roleplay should follow a less is more philosophy
As an example, let's take this fireball ability. Instead of a D&Dlike exact measurement of damage and range, I'd go with rules more open to the varied and often unpredictable situations freeform roleplaying brings. This will require an attentive GM, but would allow for much more real roleplaying. Let's say mike the fireballman wants to shoot a fireball at luke the victim for whatever reason. Mike would describe his aiming, whether he's anticipating dodging action from luke and leading accordingly, and perhaps even reason away potential manners of cover. The one targeted with an attack would then descirbe the measures they take ot defend themselves and possibly how they set up for a counterattack. After both parties have given their side of the scene, the attack is rolled by the attacker. The difficulty of the roll is determined by the GM based on the offenseive and defensive actions of both players taken, with the average result of whatever denomination of dice being thrown being the standard difficulty. Depending on how lethal you want combat to be you could also make hitting a target more or less likely on average by lowering the base difficulty of the roll.
Lastly I do understand and agree with you about the system itself. I didn't want to leave it to pure writing, because inevitably with all PvP there is one writer whos attacks are always "I hit him in the face", instead of "I aim for his face". However the dice rolls are all that are really needed.
Of course, the system as I just described assumes players would somewhat behave themselves, but it also empowers the GM as the ultimate arbiter of how these things go.