Why nevermind?
I don't think you understand how parody works. 
You're not infringing on anything, because parody protects you from everything. You "own" the game, since you made it. It's 100% parody which is 100% protected under U.S. law and there is no reason why you can't submit that game at all really. 
like i know i'm not a LAWYER but I am pretty sure about this
I think it becomes different when you start making money off it or start using it for a commercial purpose. I am fairly sure, I mean there are laws for things like likeness rights where people sue for things like someone using an image that BARES A RESEMBLANCE let alone Barkley here that doesn't just bare a resemblance but actually uses his name and image. At the moment I don't think there's any danger because it's not being used for a commercial purpose or anything, but the minute it makes any money I think that's when it starts becoming a possibility that law could become involved. I mean, at the moment you are in a position where you could probably approach cbarkley's agent and say, "LOOK I HAVE MADE THIS FAN GAME, CAN I PIMP IT OUT?" they probably get that shit all the time and when you back it up with the amazing reviews that are plastered all over the internet and the fanbase of people saying "THIS IS THE SHIT" it good be a great pr move for them.
But yeah who the fuck knows, definitely none of us?