...Cultural Marxism is a branch of western Marxism, different from the Marxism-Leninism of the old Soviet Union. It is commonly known as “multiculturalism” or, less formally, Political Correctness.
It can't be a branch of anything since it doesn't exist. The largest cultural theory in Marxist thought is the Cultural Hegemony theory by Antonio Gramsci and it describes how ruling elites manage to inscribe their values and ideas into the lower classes of society against these classes best interests.
Multiculturalism is something entirely different and Political Correctness has nothing to do with either.