I think a more appropriate question is what kind of game would Jesus play? I think a lot of people on here are confusing God the Creator and Jesus Son of God, which mucks up the issue. Jesus isn't a The Sims or Civilization kind of person. Jesus is more of a practical morality figure. That said, I see Jesus playing RPG and Open World games where you have more freedom to choose your character's path. And of course, he would choose the most evil path and get the character's life all messed up just to prove a point about it.
So with that said, I see Jesus playing XBox360. Why? Because it's a lot easier to make His point when you have a large multiplayer base made up of adolescent young homophobes. I leave it to you all to sort out the nuances of that last part.