Can game data be saved directly on the Arduboy, or save points, so when its switched off restore save points?
The Arduboy has EEPROM for exactly this kind of thing. It needs to be coded into the game though.
For a guide to the general Arduino EEPROM library, see here.
And if you’ve got the time and desire, you can review or even join the never ending discussion on how EEPROM should be shared on the Arduboy.