I've Pathfinder Adventures installed on two different android devices. A tablet and my phone (Note 4). Both devices use the same google account and are logged into the same Google Games account. I can see that the items I bought in the store and the gold I got from playing shows up identically on both devices.

 

But I would have, naively I guess, expected that my actual game state, parties, game progress and so on, would be synced between all devices. That doesn't seem to be the case?

I noticed this as well.  I'm guessing that characters and games are stored locally on the device.  On another topic, I surmised that the server resources necessary to store every game by every player would significantly raise operation costs.

Hello! This is a feature we are working on. The issue is that there are a lot of edge cases: saves overwriting saves, logged in to two devices at once, etc. We just want to make sure there is a balance between convenience, security and simplicity. ^_^