3rd party apps don't have that kind of access permissions. Only OEM and Microsoft can create apps that can access such data. Regardless, even if you can move apps to SD card using Storage Sense, it won't help you because apps on SD cards are encrypted and once you hard reset, you lost your current encryption key and a new key is generated. Those apps will no longer be useful to your phone and will be prompted to delete next time you open your phone.
So is their any possible way to save my game data?