I think the "who wasn't a Muslim" interjection he came out with may mean that he was particularly keen to present a view that it was a homophobic hate crime ...that just happened to be committed by a Muslim.
Whereas the press, and the other people on stage, we're taking the view that the atrocity was an act of religiously motivated terrorism, focused specifically in this instance on the radical Islamic hatred of gay people, rather than all the other kinds of people (i.e. most of them) that they hate.
Personally I think it is too early to say if the shooter's homophobia was the casue of his reported religious justifications, or if his religious outlook exacerbated/encouraged/caused his hatred of entire groups of people. We simply don't have enough information. We may never have enough information.
However it doesn't seem like he was the sort of person who found it hard to find groups of people to hate. Certainly his former wife and colleague's interviews point to him having been none too keen on gays, emancipated women and black people.