I didn't get anything of the above from Peterson, for whatever that's worth, but from study of primary sources and derivative materials. Perhaps you would prefer the term Neo-Marxism?
Discussion
No, because there are no marxist elements to it.
Wokism is more appropriate.
Well, OK, but there is a clear intellectual ancestry from "wokism" back to Marx, and to Hegel before him, and especially to the gnosticism that drove them both. Check out Voegelin, del Noce, Lindsay.
The Marxist element is the desire to distribute social status based on who is most lacking in status, at the expense of those who have earned it by being intelligent & competent & civilized.
Marx philosophy is the equivalent to an engineer writing a manual where he chastises physics and creates an alternate engineering philosophy where the gravitational constant isn’t considered in calcs. It’s just magical thinking nonsense.