I used Google Play Game Services for a turn-based Android game a friend and I made this summer[1]. I like to develop on the PC and have a really fast test cycle, so I made a client implementation for desktop Java using a wrapper around the REST API.
It worked pretty well, except I could never figure out how to be notified that the other player took a turn. On Android there are hooks for this, but on the PC I ended up just polling their API for changes (I figured since it was just me I was unlikely to be tagged for abuse...). Maybe "Pushtokens" is the thing to use? The API documentation doesn't say what a "Pushtoken" is.
You're right, the real-time multiplayer stuff is only available for Android and iOS right now. It'd be nice if they made a web-socket solution to handle this.
It worked pretty well, except I could never figure out how to be notified that the other player took a turn. On Android there are hooks for this, but on the PC I ended up just polling their API for changes (I figured since it was just me I was unlikely to be tagged for abuse...). Maybe "Pushtokens" is the thing to use? The API documentation doesn't say what a "Pushtoken" is.
[1]: https://play.google.com/store/apps/details?id=com.infinite_i... -- it's inspired by Letterpress. I wrote up some of our other experiences building the game, too, since I did a custom toolkit and physics engine for it: https://medium.com/@i_am_ralpht/building-letterplex-1-0-a78c...