A hash of the inputs can't be used to replay the game and thus verify what happened. You'd need the full input list, including mouse movement. In my experience FPS games send around 200MB/h in networking, so assuming only a 1000th of that is needed to store the inputs that comes out to ~5600USD/h. Even if it took just a kB that's still ~30USD just to play the game for an hour. (This of course ignores actually running the game inside a smart contract, which would also take an obscene amount of gas)