Whilst I'm sympathetic to the overarching point the author is trying to make (Lenin bad, more so than is generally appreciated), confusing Georgy Chicherin with Boris Chicherin does not build confidence he is the best person to make it (or in the editorial practices at New Criterion).
There is some truth to the theory of "cultural Marxism" but it's usually presented in an unflattering and conspiratorial light.
Gramsci, a prisoner of Mussolini, questioned why Marxism had failed to foment revolution in the west. He came to the conclusion that the working class were indoctrinated, and that a "counter-hegemony" of thought based on progressive values was necessary to grow a more egalitarian society.
Herbert Marcuse, perhaps the defining philosopher of the 60s, continued this line of thought. There was no conspiracy or deception, however, since Marcuse was an open Marxist. He had a significant impact on the radical culture, and the sexual revolution of the 60s.
In this sense, if you are opposed to "cultural Marxism," then you are opposed to the cultural shift of the 60s. Personally, I think the cultural shift of the 60s is to be celebrated.