Clark Wendell is NOT benefitting from any form of "gay privilege." He is benefitting from "white male privilege." The fact that he happens to be gay underscores the sociological circumstances that have forced him into the closet in the first place.
You are right when you point out that gay White men benefit from unearned privilege vis-a-vis the rest of the LGBT community...but that privilege is due to us being White and male -- NOT due to us being gay.
Calling it "gay white privilege" is intellectually-dishonest when the nature of the privilege itself has everything to do with race and sex -- and nothing to do with sexual orientation. Being forced to congregate "underground" with other gay men is NOT a privilege.