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).

I think you're right, Tabletop Simulator gives you an environment to do anything but doesn't help you define interactions and rules as far as I know.

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.