Would be really nice if you guys could have a WebAPI like Steam, so Sites like AStats can track our Achievements on GoG, like they do on Steam. Of course this should be subject to privacy and it should be opt-in. But I personally would enable that in a heartbeat.

I think it would make more sense to simply provide these stats directly on GOG / in Galaxy, of course only optionally for individual user data.

No. I want them to be trackable, like on Steam.

Example: http://steamcommunity.com/id/scorcher24/stats/appid/251570/achievements?xml=1
Those are my achievements for a game.

Now I can go on AStats and track them, compete in Leaderboards or even write guides.
http://astats.astats.nl/astats/Steam_Game_Info.php?AppID=251570&SteamID64=76561197978037893

This functionality of Steam has spawned a lot of Achievement Hunting Communities over the years, AStats being the most consistent and durable so far.

Yay, we want more trackers, we want more Steam!

It would be useful, especially combined with privacy controls to control who can see your achievements. It would also be great to have an API for owned games, and a public OpenID login. That would help to facilitate 3rd party services similar to AStats and Steamgifts developing around GOG.

I personally would not opt-in but I think this would be useful for those who want it. GOG could do it.

There is probably already a wish on the wishlist for that.

Yep.

https://www.gog.com/wishlist/site/implement_an_open_achievements_api_for_games
https://www.gog.com/wishlist/site/document_the_api_so_third_parties_can_use_it
https://www.gog.com/wishlist/site/achivment_api

Galaxy (the by now infamous GOG client) only uses RESTful API calls to fetch data, so there's plenty of stuff publicly available in theory. As for achievements in particular, there's this (but you need to go through this first in order for it to work): https://gogapidocs.readthedocs.io/en/latest/galaxy.html#gameplay-gog-com