I think the form of 'grammatical joke' he has in mind is when we make a move in one language game that would be absolutely perfect in a different game, but is totally wrong in the game in question.
Like the Monty Python argument about whether the argument being paid for qualifies as an argument, and not just flat contradiction, even though it consists of different phrasings of a flat contradiction, the starting of which causes the customer to be charged for an additional argument.
The notion of paying for argument as a performance wraps around and becomes absurd, the one is part of one kind of reality, the other is part of another. At a certain level, the very best form of this kind of humor do strike me as deep, until I unwind them. And the misunderstanding, of course, needs to be novel. Another take on the used trope does not work over and over again.
He references this kind of absurd performance as a joke in the Blue Book, and I am pretty sure this is still the general idea.