Most games are system specific. Like...I was digging through my kindle's files, and found a bunch of game files that save progress and stuff. I don't think Game Center (Game Circle on kindle?) saves the game progress, only what your trophies/achievements are. Alternatively, the game is not a Game Center game, and therefore was not compatible to save backup. Idk, Game Circle on kindle doesn't save progress, just achievements.
The only game that I know of that saves your progress is SImpsons Tapped Out if you have an Origin account.