I think it is a weakness of the article that PG does not address this directly. He dis say that racism is
> Not a problem on the scale that the woke believe it to be
So if someone only uses woke to mean "being aware of and attentive to important social issues" it is easy for the to wake away with the impression that PG painted their concerns as overblown.
If I was PG's editor I would suggest replacing 'woke' with prig here for clarity.