hmm I don't know what to say because for me if I do uninstall and install, my game save is still there, regardless if the game save is done through server or in the device it self. I used to own an iphone 3G up to iPhone 4S and in those times when I uninstall and reinstall the same game, the saved game is there. Only time when it doesn't is when I do a factory restore and set it up as a new device. With the iOS when you have the back up, it saves your game saves, so even if you were to restore from back up, you get your game saves back.
Sorry I do not know much about android since S4 is my first android phone, previously I have been using the iPhone 4S (therefore I know a lot more about iOS devices, not android). Even if I did a factory restore and restored from back up on android, it seems like it only restores contacts, I literally have to re-install all the apps manually, which is a biggest CONS for having an Android for me. It's not big of a deal at this point in them but when I get more apps then it would be a big deal.