The Anderson Cooper example is good: If a right-wing blog always showed images of Cooper photoshopped into drag, we’d take it as an attack on gays.
Is this different? It’s really hard to disassociate the question from my emotions that “yes, this is different, because I don’t like this guy.”
Part of it, of course, is that it’s attacking the excessive masculinity of Trump’s image and that of his supporters (contrast Cooper actually being gay). I mean, this whole video is in the context of his abusing women. Part of it is that he does have a surprisingly high voice. Part of it is that we feel like we can mock a campy voice without mocking gays (see Liberace, above). But the latter two arguments wouldn’t hold water in the Cooper example.
For me, the real justification is that, like @Fef above, this is just about the only way I can tolerate listening to the schmuck. (Maybe the campy voice actually raises my estimation of him while I hear it. I dunno.) But again, not much of an argument, it’s true.