Using the model of attractors, I think for ma a “social game” is one that’s more social than anything else—bearing in mind we’ve already talked about negotiation games, and they’re a different thing.
Are social deduction games social games? They’re showing on up several people’s lists. To me the key there is that you don’t have enough information to solve the puzzle, so you have to work on your reading of other people to fill in the gaps. But they’re not the sort of game where you can have an ongoing conversation, and over to the side the game gets played.
The way I play Crokinole is very social, but I bet that’s not true for more serious players.
In a wider sense, I suspect I’m not the only person here who can’t abide general undirected socialising - the sort of party where you’re expected to chat to strangers for only a few minutes at a time then move on to someone else is a thing I abhor. That’s not why I started boardgaming (or role-playing or SF conventions), but there’s a desire that they all satisfy: something approximating a common reason to be there, and enough time that one can have an interesting conversation about something rather than just superficialities.