That comment actually says "heterosexuality is normal", which is of course ambiguous - it could mean either of "prevalent" or "not merely prevalent but standard, with deviations from it being seen as undesirable". Heteronormativity might be a description of the latter claim, but denying that heterosexuality is especially common is mere wishful thinking.
The claim that gender and sexual orientation are linked would've been quite recognizable to ancient cultures including classical Greece and Rome, where heterosexual behavior was not normative and other sexual arrangements were often celebrated (though their dark, exploitive side, linked to the ubiquity of rape culture as purposeful male domination, was not unrecognized either; and this later fed into Christian condemnation of such practices). So it makes little sense to view that as "heteronormative" either.
I make no claims about heteronormativity in Greece or Rome (I do say that the patriarchy is several millennia old, so this could be read as an implicit claim that patriarchy existed in Greece and Rome [and I wouldn't take issue with that claim], but I don't think you'd find this disagreeable, given the "rape culture as purposeful male domination" you reference, and that the definition of patiarchy I provided specifically calls out the domination of men), and gender and sexual identities certainly are linked in the sense that certain combinations are more common than others - they just aren't synonyms. As I noted, there is no burden for this concept to translate to other cultures and time periods in order for us to accept it as a useful model for the purposes of our discussion; I've not seen a counterargument from you on this, so I don't see why I would accept these observations of Greece and Rome as being deleterious to my point, anyway.
Heteronormativity is just heterosexuality as a normative element of social structures (not merely prevalent in society, but where deviation from it is viewed as transgressive.) In modern societies, it is typically tied to patriarchy (a particular normatige structure of gender roles, in which social power is attached to male roles), cisnormativity, and, in particular societies, it may be attached to things like White supremacy that are superficially farther from sex/gender dynamics, but these are nevertheless distinct if linked elements of the cultures they appear in.
But we certainly agree that heteronormativity is different than society having a majority heterosexual orientation.
Note that by this standard, much of LGBTQ+ culture might well be described as heteronormative, since glorifying social transgression as such (not merely inasmuch as it might inevitably follow from having a non-majority gender or sexual orientation) has long been a staple of that particular identity.
Heteronormativity isn't an epistemology, there's no burden for it to be consistent. It's a set of beliefs and attitudes, and a label that allows you to critique them. Why would we expect that to be any more consistent than the human behavior it describes (which is to say, only somewhat)? Will this label break down and stop making sense as society changes? Yes, I imagine it will. Will it become unwieldy and eventually fail altogether if we employ it in an analysis spanning cultures with very different conceptions of gender? Absolutely. But you might as well ask whether the concept of pop music is consistent and relate it to the works of Beethoven, if you think that's useful in your analysis than go for it, but if it doesn't work in that circumstance it isn't a condemnation of the idea. The only burden on heteronormativity is to be useful in describing real world behavior, which it clearly is.
If you want to know whether heteronormativity is a real phenomenon, you need look no further than the comment I criticized. It doesn't say, heterosexuality is prevalent; it says, heterosexuality is total, that it is "natural" and "normal", that it is inseparable from gender, and that people living as (or even describing) other gender and sexual identities are doing it to trick you.