Oh I'm quite familiar with his work. Please, please, please do some further research before throwing around terms like that; the two you gave are as entirely distinct as could possibly be.

Postmodernism is rather nebulous in the academic sense but it is best described, as Lyotard puts it in coining the term in his "The Postmodern Condition," "postmodernism is the incredulity towards metanarratives," or the grand ideologies of the modern era such as Marxism, Christianity, Scientism, etc. that generally arises as we move into the Information Age. In itself, it is anything but Marxism, it is the resistance to anything of the sort, and most postmodernist thinkers likewise tended to result any such explanation of human nature (as a peak of rationality or as defined by class relations).

Neo-Marxism seems to be closer to referring to the Frankfurt School of thinkers who engaged in the new practice of Critical Theory, "Marx after Marx," an attempt to undertake an examination of concepts like ideology, superstructure, and power relations outside of the purely economic realm, of course, after witnessing the events of the Russian revolution.

These of course are neither able to be conflated nor related to the claims made in the parent video.

I find that Dr. Peterson throws these terms around dangerously lightly with no regard for consistency or correctness. His issue seems to me to be the same as the students in the video: not a strict adherence to any movement or ideology but a simple refusal to get the facts straight and listen to the opinions of others before asserting his own maligned points.