Short answer: No.


Long answer: 

Antisemitism is a category of hate. Essentially a sub-category of racism in general. That leads to this statement: All antisemitic people are racist, not all racist people are antisemitic.

Cultural Marxism is an ideological anti-conservative conspiracy theory.
A conspiracy theory can be hateful in nature. The conspiracy theory is geared towards things conservatives hate, but it is based on the thought leaders exported from a school, not a group of people.

For the two to be inherently tied, the origination of the theory must directly link to Jews or Judaism first. The argument from the NYT piece is that it is an old, and clearly antisemitic conspiracy theory, was updated. While that can be true, the update is a clear departure from the antisemitic tones to a more generalized hateful tone. This is to say "Cultural Marxism" can be stated as inherently racist (or hateful), but not inherently antisemitic.

There are a great many antisemitic people in this world in just about every group of people. An unfortunate truth. But the school, people from the school, and thought leaders were not all Jewish. Even so, being of Jewish heritage doesn't necessarily mean the person can't be antisemitic. Likewise it is possible for a specific group of Jewish people to be hated independently from Jewish people in general. 

Given that it is a conspiracy theory it is easy to tie to fringe groups or ideas. Which, when attempting to demonize it, would be easy to associate with antisemitism due to the time and location of many of the people at its origin.

However, many theories or groups can evolve over time. This can cause some concepts to become permanently associated. So it is possible for Cultural Marxism to evolve into an antisemitic form, if a branch of it isn't already there.