To get to the chinese checkers thing, I bet chinese checkers and parchisi were the family games of their time, and I bet at some point they did have a theme.
Family games yes, but I doubt much in the way of theme. Sorry never had a theme.
Does Mah Jong? Poker?
Never played Mah Jong, but I wouldn't call poker an abstract game. Its in another category as far as I am concerned. Betting game? Gambling game? Not an abstract though because its not abstracting anything.
We could get all philosophical about why we even need/want these categorizations at all. I'll save that for another time, but I think that would be a good discussion to have.