Let us start by recalling what postmodernism is and Mr Peterson's stance on it.
Postmodernism posits that different interpretations of the world can be equally valid and be at odds with each other, and rejects the notion of objectivity and meaning.
My interpretation of Mr Peterson's position is that Marxism, despite being opposed to postmodernism in some important ways, nevertheless derives from postmodernism with the added cynical supposition that all interpretations can (and should) be seen as a struggle for power. He condemns this as an inherently violent and counterproductive view. Furthermore, he rejects the idea that all interpretations of the world are equally valid, rejecting the premise of postmodernism.

This is a highly condensed summary of a complex and nuanced topic which is highly debated amongst philosophers and intellectuals, and the concepts of postmodernism and Marxism themselves are open to interpretation. Therefore, my summary may be flawed.

To answer your question, I don't believe anyone can give a definitive answer as to whether Mr Peterson is correct or not. In fact, the postmodernist view might reject the idea that the question has an objective answer. However, I can highlight the fact that Mr Peterson's interpretation of the relationship between postmodernism and Marxism is contentious, and not everyone whom he describes as postmodernist openly identifies as such.

If you'd like, I can direct you towards resources on the subject of the relationship between postmodernism and Marxism.
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