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.
> 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.
If you believe that single sentence (that I disagree with him about, but that's neither here nor their) is the entire point of the article, I'd really suggest you read it again, it's far more interesting than that.
