Well, it would be a co-op game with lots of puzzle, platforming, and party-game elements, and every time your character runs across another puzzle they start exclaiming about how stupid the game is 'cause they were spending too much time joking with the co-op partner and can't figure out the puzzle.
The Barrynator would be taunting them throughout by changing around the game world, making things suddenly appear, disappear, rewind, fast-forward, etc.
All tutorials would pop up on the screen but scroll through too fast for the player to read, and the player characters would talk to each other outside of the context of the game any time an exposition dump occurred.
There is no fourth wall in Game Grumps: The Game.
And it would spawn a sequel entitled Game Grumps: The Game: Even Grumpier.