Actually I had a similar idea about 2 years ago and started implementing these four games (Backgammon, Checkers, Connect 4, Tic-Tac-Toe) on https://games.z-mans.net/.

But there was no real acceptance. Apart from my beloved playmates Botox and Honey 40 people registered - but only 11 played at least 1 game.

There was almost no feedback on the games, instead I received countless questions on how to port the old Facebook theme. That was just annoying, so I stopped the development.

Perhaps these kind of laid-back board games are simply outdated. At least a lot of today's gamers seem to prefer killing instead of thinking.... :)

I don't think you're going to find anything that's a true "turn key" solution since OSSN uses its own standard for logging users in and (optionally) storing their login credentials. You might want to have a look at how services like auth0.com integrate other services (social logins, in this case) with their own backend functionality. Also, this post from Stack Overflow might help to understand what's required when trying to integrate information from 3rd party apps (or games, as the case may be): https://stackoverflow.com/questions/48335509/login-with-facebook-or-google

I'm aware that you're not actually asking about using a social login to login to your OSSN site, it's just the best example I could think of that deals with integrating outside data into your OSSN site.