Yes, that is a fair point and one I’d missed a bit from your original post. I appreciated the scare quotes in the article but you’re not wrong.
That said, I don’t know if you’re exactly right either. “Woke” was co-opted by the fash. I don’t think we should just let them have it. A good starting point is for every interlocutor to stop them and ask them to define the word every time they use it. The word is not the problem.