On Beach Buggy Racing 2: You can back up and restore your game by securing your account with an email and password.

For all other games:

Your game will be backed up using your iCloud account. Be sure that you are signed in with iCloud in your System Settings. Your game will be saved to iCloud, and you can restore it after resetting or changing your device.  Just make sure you are signed in with the same account in iCloud.

To cloud sync your game:

When you start the game on a new device with cloud syncing enabled, you should see a message box telling you of a save game conflict, and asking you to pick which game you want to keep.  Typically you should choose the game with more progress (on a new device, this should be the cloud game.)