Everyone wants to have their cake and eat it too. Enkidu is either male, therefore GilKidu is BL and should be tagged as such, or Enkidu is NB, and therefore GilKidu shouldn't count as yaoi or BL despite everyone saying it is. Pick one. You can't have both.
I am not NB myself, but I am trans and I have had similar conversations with my fellow NB siblings about how they classify their own relationships. Ultimately, it is up to them on how they classify them, but most consider their relationships, due to the fact that they are NB, to be queer. A good example would be to look at the term NB lesbian, for example, which has become more and more prevalent.
Anyways, I am in no ways an Enkidu expert either, but GilKidu since its inception in The Epic of Gilgamesh has always held that queer relationship too, whether or not you believe that Enkidu in the Epic is gendered male or nonbinary (however most people I’ve spoken with tend towards seeing Enkidu as nonbinary.) Furthermore, the game, at least in its English localization, firmly lands on non-binary or agender, and Enkidu uses they/them pronouns.
I am ultimately no expert in either field, of Enkidu or of being NB, but I can pretty confidently say that Enkidu being NB does not mean that GilKidu is not yaoi or BL, as relationships with nonbinary people can be defined as queer.
So yeah I think fans can have their cake and eat it too, in this situation.