Have you looked at Vassal? https://vassalengine.org/

It's a board game engine and has multiplayer support. There's also boardgame.io which looks hipper (npm), but I didn't see any screenshots of games being played.

Regarding scaling, there's articles about lots of stacks doing 1M websockets on a host; if that's limiting you, you've got a lot of players, so that's a nice problem to have.