All board games have something math-y underneath them. There is a thing called Game Theory, after all.
But for some board games, the theme around the game aids our intuition about how to play the game. In others, it serves only as window-dressing.
Take, for example, Settlers of Catan. We could change the theme somewhat, but fundamentally a theme around resources helps players figure out what to do with the cards. Saying that "ore helps you build buildings" also helps new players understand and recall the rules.
It might be the exact same game if we got rid of the metaphor and just said it's a game where you can exchange three grey cards, two yellow cards, and an S token, for a C token, but that would make the game much harder to learn and play.
At high levels of play perhaps you might spend all your time thinking about card draw percentages and see the board as an abstract graph, but the theme won't get in your way.
I'd say similar things about Agricola. Or the 18xx series of games. Those themes really help most players learn and play the games.
Other games, not so much. Ticket to Ride would likely be just as easy to learn and play if it was an abstract game of network connections. Go and Chess are clearly long past their original themes. And so forth.
So getting back to your question, I'm trying to say something beyond "All games have an abstract game underneath the theme." I'm trying to say that "A large disconnect between a game's theme and its underlying abstract game is not rare." I don't claim it's universal, but I suggest it's not so rare that Scrabble stands alone as an oddity.
JM2C.