This is why I point out that an absurd statement still points toward meaning via a metaphor or language game, which I would put wordplay/jokes under the rubric of.

In fact, in my thesis, I cited The Naked Jape, by Jimmy Carr specifically in reference to jokes (it has a one-liner on every page). On of my main arguments against Gricean conversational implicature theory was that the theory itself was a form of begging the question or no true scotsman problems, in that all of the obvious examples where a counter-factual to the cooperation principal that exist everywhere are excused as "not conversation."

https://archive.org/details/nakedjapeuncover0000carr

Again, yes, you can have wordplay, but wordplay is wordplay, and is a language game that exists and is trying to do something in a different framework.

The reason why so many folks have no issue with the puzzle is that they view it as a puzzle (a kind of language game), and not a sensible human communication. This lets them genuinely consider absurd statements and treat them as normal.