Oh, I was hoping for a DSL for prototyping the rules to play these kind of games on a computer (and perhaps train a neural network as an AI opponent). I've been working out how to do these things recently.
Correct me if I'm wrong, but isn't Tabletop Simulator only about physical simulation? VASSAL seems much closer to what parent is looking for (but there's still very little on the rules verification front there).
As far as what you care about most games go, a chat room with the ability to send private messages to each other and a (human) game master is all you need to play almost any game online, if you don't care about automated rule verification.
I once wrote a multiplayer cardgame server (with a friend) that provided a Game API[0] to Lua scripts to define state and behavior. We scripted multiple card games popular in my country. For example Ace's Up[1].
We also wrote a few clients (ncurses, android, flash), most of them remained unfinished/unreleased, including the server, unfortunately. I meant to put it on GitHub but still hesitating since it would only be for educational purpose and no real interest in pursuing the project much further.
Just watched his talk, def worth a watch (Thx for the link).
The repo is below, he added disclaimers that it's rough code and was enough to help him make some useful decisions mainly around game length and balance as he developed his game.
