That's not the author's main point — the author's point is the surprising observation that “That joke isn't funny any more”, even to the author himself. This is something deeper than the usual “genre of argument” you're referring to.
Eh, he goes out of his way to say
> The good news is that I don’t think that the illiberalism of identity politics will endure much longer. Especially when it comes to the literal policing of humour - and cancellation of comedians for telling the wrong kinds of jokes.
I think it’s still his point.