Yes I think he is saying he's fed up of straight people identifying as queer (and possibly by extension all the other people identifying as things they're not) because words have meanings, something he cares about as a writer, and because he's gay, which also matters to him.
I think there may also be an element of being arch and intellectual about it in a way that ideologists/the TQ lobby won't find it easy to pick apart, so they won't be quite sure what side he's on. He's not saying "yay go rowling!" is he. (Not that he should - but my point is if he wanted to lay his cards on the table unambiguously he could do that easily enough.)