Soral was against the EU and has always had a thread of nationalistic pride, I can somewhat see the picture you are trying to paint but I have to disagree. Straight from the horses mouth
Soral is very much so interested in a non-globalist world that doesn't take peoples economic output as a matter of divine right. It's how he could start in a communist party and end up on the far right. Soral sees Nationalism and self reliance as an easier way to establish a monopoly of labor and true personal autonomy. Your view is of the US politics in service to US needs and within US borders, but part of modern socialism and capitalism is that both are in service of the globalization of economies. Soral figured this out and made the transition from global marxist to local nationalist. The name is different but the sentiment is the same.
You aren't presenting evidence of the absence of marxism, you are showing coercion to labor by the abolishment of preexisting social norms. When a monopoly of labor profits is created in a marxist or capitalist system there is a group of people that benefit more than others. The true elites, and the complicit middle or nomenklatura. In capitalism the authoritarian absolute power doesn't exist, but the cold hard realities of economic coercion do. Liberal capitalism sans conservative ideology with a dash of nationalism gives those institutions you mentioned free reign. International communism is not a realistic possibility, and supranational courts and alliances give government officials outlets to circumvent democracy and public sentiment.
What I mean when I say cultural marxist or marxism is that the actions are leading to an inevitable one way path towards a more desirable outcome. Obamacare was foot in the door Universal Healthcare, that required immediate subsidizing by the productive. Feminism performs what both capitalists and socialists desire, increases economic output that benefits elites of both groups. The answer to the ponzi scheme of social security? Improve the fertility rates and increase immigration! Both ideologies benefit from pedal to the floor economies that never ease off the gas.
Nationalism and classical conservatism seeks answers from within and not cheap quick fixes that will fall apart down the line. There is a definite overlap between anglo capitalism and marxist systems, that doesn't mean that the end goal of those that identify as socialist humanitarians isn't marxist in nature. Marxist solutions inevitably lead to marxist wealth redistribution. This is a reality in Soral's home country of France where they attempted to implement a Super Tax to reduce the burden of the system on their low earning but productive citizens. Profits from socialist countries aren't staying within their borders, which wouldn't be a problem if there weren't people that took more from the system than put in. This problem is even worse in Capitalist countries. All you have to do is look at Russia to see what happens when the profits from within a country move to the bank accounts of oligarchs and outsiders.
Soral's stance in the context of French politics makes sense, Nationalism is his answer to the exploitation of his non-global compatriots. A very marxist sentiment arrived at because he can't support coerced labor (the example from your feminist video) and unanswerable totalitarian leaders. He's a man that has thrown his hands in the air after years of idealistic and naïve thought and chosen France as his only concern. For his philosophy he has everything he needs already, he just has to figure out how to not coerce but cajole the unproductive, and keep profits from bleeding out of his country.
A tall order.
TLDR Cultural Marxism is a thing.