It is also much more than that. While he is being disingenuous, he isn't really wrong in a basic sense.
There are "Marxist" approaches to all kinds of things: politics, economics, literary and art criticism, historiography, cultural studies, etc.
This is completely uncontroversial, or at least was until US Republicans started to bandy around terms like "cultural Marxism", which made some people reflexively deny any link.
While the term 'cultural Marxism' is often the equivalent of Hitler-ing someone by creating connotations of Stalin et al., there is obviously a Marxist/Marxian influence on these things.
Critical Theory certainly was influenced by Marxism, and underpins much of the Progressive ideology currently faddish. Ditto the field of cultural studies which has been massively influential
Can look at the history yourself, for example:
Centre for Contemporary Cultural Studies - Wikipedia
Obviously there are many more influences and it is reductive to simply see it as a continuation of totalitarian Communism (much of it evolved among the more anti-authoritarian Marxist intellectuals).
I don't think calling it cultural Marxism is either helpful or operating in good faith, but denying that it has been influenced by "the study of culture through a Marxist lens" seems wilfully obtuse.
Obviously polemical, it is both misleading and very roughly correct (although has acquired numerous exaggerations and fabrications that border on conspiracy theory territory that are not roughly correct).