So they abandoned Marxism for a different ideology and you think that makes Petersons's point that postmodernism and marxism are the same thing? Come on.
He never said they're the same thing, that's a strawman.
Zizek, a Marxist, even tells Peterson in the video MH posted that he agrees with the main point he's trying to say. He just asks "where are all these Marxist postmodernists"? Uhmm has he been inside a university classroom in the last 10 years?
Critical social theory, postmodernism, and intersectionality have all built on each other over the last 100 years. I would say postmodernism is the least political of the three theories. As you say, postmodernism would actually reject Marxism as a meta-narrative. It's really more accurate to call progressives today intersectionalists or critical social theorists, or people using postmoderism in a political way (which is a bastardization of postmodernism). Even intersectionality isn't inherently political. Breaking down some social phenomena by race, gender etc is simply a way of seeing things through different lenses and breaking down humans into different variables. But people inevitably put a value judgement on variables they see as oppressed categories (racial minorities, women etc) vs the privileged (male, white). Intersectionality is a popular theory increasingly seen in university classrooms over the last 10 years, and IMO has been politicized, with oppression and privilege being added to its definition and co-opted by feminists and other groups for political agendas, for better or worse. I think it describes today's "woke" ideology very well:
https://en.wikipedia.org/wiki/Intersectionality"
Intersectionality is an analytical framework for understanding how aspects of a person's social and political identities combine to create different modes of discrimination and privilege. Examples of these aspects include gender, caste, sex, race, class, sexuality, religion, disability, physical appearance,[1][2] and height.[3] Intersectionality identifies multiple factors of advantage and disadvantage."
So anyways, we can argue about definitions and terms, and we can argue that Peterson should use term X over term Y, but as Zizek says he knows the point that Peterson is trying to make. I'm not arguing he can't make his point better. He could maybe use a better word than "cultural Marxists", but most will know what he means when using the term.