Etymology isn’t the best source of information on ideology. Also, the identification of “non-binary” as a kind of gender isn’t itself a theory of gender, any more than being male or female is a theory of gender. A lot of non-binary people adopt that term to make their identities more comprehensible to a general public whose ideas of gender are binary by default, and because our language doesn’t supply an appropriate ready-made term for their gender. It’s like how I call myself a “non-traditional student” because although my existence proves that the “traditional” understanding of university students as attending one school full-time from the ages of 18–22 and graduating after four years isn’t universal, that understanding is pervasive enough that my existence as outside that norm is more easily explained and accommodated as distinct from it.
There are plenty of people who identify as a binary gender, whether they fit all the stereotypes thereof or not, so there is evidence of a somewhat binary (or bi-modal, at least) distribution of gender. Non-binary individuals simply don’t fit into that distribution as neatly as the majority.