I don't really think that's the case. It just refers to a subset of rights associated with a particular segment of the community. Like reproductive rights, or press rights, or children's rights, or whatever.
I disagree because reproductive rights, press rights, those aren't describing an actual immutable characteristic of an individual, it's an actual "thing". Gay isn't a thing, it's an immutable trait. And it's one trait that is one part of what makes up who we are as individuals. We're human at the end of the day, not a sexuality. That's why I use the term human rights when discussing equality more often than not. We're all human beings, we all bleed red, and all legal citizens require equal rights, that's what it's all about ultimately.