Each game does it differently, so there is no fool-proof “universal” way to do this. For each game, you would have to know where each game save is stored, and share that file between devices, assuming of course the game itself doesn’t have any cloud save functionality.
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The way it works is that you have to pick your games from a list of known games. The list is easy to expand as long as the application know its strategy. At the moment I've checked 5-10 games and they all use a similar strategy. For most games, once you tell my application where the executable is located, it will be able to store the saves on the cloud.