Since no one has provided their take on this question this is mine.
I personally wouldn't count this as a counterfeit as its not trying to reproduce or copy an existing note. The design is completely unique, and it does not appear to be trying to fool people. I think this is just the Houthi governments way of attempting to appear legitimate on the world stage.
I would consider this note as a standard issue. I think of this situation the same as I think of China vs Taiwan. Country divided between 2 competing governments as a result of a war, both claiming the latter's territory, and both having various degrees or international recognition. Notes from both are treated as standard in the catalog (albeit Taiwan being classified as a state with limited recognition). So I would think the same treatment applies here.
That is my take on your question if my lack of expertise means anything. I am just happy I was able to get my hands on one of the Houthi notes