I didn't need to define woke, because the person in the article outlined what they perceived as woke; this being the very next part of the article where I break down what exactly they are describing as " woke." I mean that was kind of the point, I have seen woke used to describe a myriad of things, so it is important to instead use the context and explanation of the individual in order to figure out what it actually is I am arguing against.
The argue didn't engage with a debate on wokeness, it engaged with a debate on the points that he was claiming were woke. This entire initial point is kind of an aside -- as you expressed somewhat, it is relatively irrelevant. Also seems as though my context-driven definition parallels the actual definition, so if I got the definition right in the first place then I do not understand what the problem could possibly be.
The article didn't criticize woke, it criticized what the author describes as woke. And the word woke, or its definition, is irrelevant to that. This entire point, showing that it was wokeness that caused this shift, was an aside to segway to the actual arguments against the other arguments. Wokeness is not an argument, so I am not arguing against it.
It's just an adjective. It is irrelevant to the arguments. For example, if he were to say " these stupid gay rights are infringing on someone else's rights" and I were to not know the definition of stupid, this would not negate my ability to argue " gay rights are infringing on people's rights," because the adjective is not the subject nor the predicate.