"Cultural threat" is not correct descriptor of "elimination of white race". They were talking about race war, you are trying to find words that make it non fascist. So, you will need to be precise about what your euphemism of "real cultural threat" means. If it means that they perceive Jews as the reason for "elimination of white race" as they said, then it is just being Nazi with all the logical consequences.

Some people are Nazi and that is that. The eternal wish to reframe far right nazi as something else and non-threatening regardless of what these people do, say or push for amounts to lying to oneself.

I guess I got the answer then.

They did not mention a war. You can eliminate a race without a war or violence.