According to the Source of all Knowledge, Wikipedia: "most commonly, nihilism is presented in the form of existential nihilism, which argues that life is without objective meaning, purpose, or intrinsic value."
The logic of "marriage equality" is thus: Gays and straights must be treated equally under the law. Therefore, it is invidious discrimination for the law to treat opposite-sex couples differently from same-sex couples. Therefore, the dictates of equality demand the legal recognition of same-sex "marriage". But for the law to effect this equality between straights and gays, it must say that the difference between the two is not sufficiently relevant to justify differential treatment. The difference between the two is rather obvious: the former desire to engage in an act upon which the endurance of humanity has hitherto depended and the latter do not. To say, therefore, that this difference is irrelevant in the determination of public policy is to say that the endurance of the public does not matter.
One can argue that this does not follow at all because the advent of Artificial Reproductive Technology now enables societies to ensure their endurance without relying upon the heterosexual act. Thus, the heterosexual act is in principle unnecessary to the perpetuation of humanity as a species. It can now simply be regarded as merely an expression of intimacy and as such no different in kind from other such expressions, ranging from cuddling to frottage to building pillow forts, thereby eliminating the only significant difference between opposite-sex and same-sex relationships.
Nevertheless, the heterosexual act, coitus, remains the only natural way for humans to reproduce, and to say that this is trivial, nugatory, and irrelevant to how we should order society entails the view that Nature has no prescriptive force. For if Nature's way to replenish human society is irrelevant, then we might as well say that Nature is indifferent to our very existence. Nature really doesn't give a shit about us at all.
So what? We care about our own existence. We care that we will continue our existence as a species, and it really doesn't matter if we do so by the natural way or by Brave New World technologies, that allows us to have really fun NSA (No Strings Attached) Acts of Intimacy. So long as we continue on. That's what counts. Nature doesn't care about us, and we shouldn't care about Nature.
But if we've decided that Nature really is indifferent to the endurance of humanity, then we must rely only on our own opinion that it matters that our species lives on. And opinions are changeable, fickle things. Opinions that once enjoyed a virtually unanimous consensus and for centuries taken to be axiomatic (like, say--oh, I don't know--, the notion that marriage is the union of a man and a woman) have been known to change dramatically and in less time than it takes to complete a degree in marketing. Yeah, okay, most of us think it's important for us humans to carry on, but that's right now. We could change our minds later. Maybe, in the near future we decide that Nietzsche and his epigones the Transhumanists are right and that humanity as we know it should perish to make room for a race of Übermenschen. It could be a genetically modified form of Aryans with an extra blue eye as a spare or something like the Daleks or, perhaps, the latest new iPhones endowed with crazy super Artificial Intelligence. What would be the objection? That it's not natural? Please!
Saying that Nature is indifferent to humanity's survival is tantamount to saying that humanity's survival has no objective value at all, that whatever value it has can come only from our sentimental fantasies. This is the conclusion to which the logic of "marriage equality" leads, and how this is not a textbook example of what Wikipedia defines as existential nihilism, I really do not know.