Titus is a game that calls itself a "political simulator," featuring an agoraphobic watchmaker who decides to run for president in the crazy world of Wealland. If that description and the game's Tim Burton-esque aesthetic haven't won you over already, then you and I have very different tastes in gaming.
The actual gameplay is more about how well you do at minigames than actual strategy, but it's a fun affair, providing a tweaked parody of politics and that really interesting art style. Titus' main opponent is a mime, and through minigames that have you catching cash or Doodle Jumping-your way along, it's your goal to win the hearts (or at least the wallets) of your people.
Titus has achievements, but unfortunately it isn't directly Game Center enabled