on season 7 episode 4, does the game that house was playing on xbox360 actually exists?and whats its name? (at 10:21)

That game does not exist for the xbox360. It was a made game that was first shown in season 6 eps 3 (Epic Fail) about a game designer who got sick. During "Epic Fail," Taub and 13 were shown playing the game for a bit.