racists are generally stupid people, and they're wrong in a lot of ways...
that said, i think the article kind of...the argument they're presenting sounds less like richard spencer and more like bill o'reilly, or maybe jordan peterson, this idea that christianity is fundamentally white and european civilization was built on it.
it's a common trope on the regular old right, and it's absolutely wrong to it's core, in every way.
1) christianity is not white in any way. it was invented by jews, popularized by brown middle easterners and then pushed down on the north of europe by italians that were every bit as brown as the jews that came up with the whole pile of bullshit. christianity initially hit it's highest point of popularity in egypt in the late classical period; western europe wasn't christianized for hundreds of more years, and northern and eastern europe weren't christianized until the fucking renaissance. not only is it not the case that europe is christian in culture, but most of europe has no substantive history of christianity before the year 1500 at all.
2) the institutions (legal, political, etc) that exist in europe are roman & german in origin, not jewish or christian. even the papacy is a fundamentally pagan institution. this is a common argument by conservatives, this idea that christianity is at the crux of our legal system. it's just plain out, straight up fucking wrong.
3) the history of european ethnogenesis is long and complicated, but the contemporary concept of europe - human rights, democracy, etc - came out of a total reversal of christian attempts at colonial dominance in europe. the kind of white identity they're hinting at is defined in opposition to christianity, not in coordination with it. it did not exist before the renaissance, and developed largely as a result to reclaim the culture from the christian dark age.
it's not just nietzsche they don't understand, it's the movement of history, in general.
but this is a better takedown of jordan peterson or bill o'reilly than it is of richard spencer.
https://www.vox.com/2017/8/17/16140846/alt-right-nietzsche-richard-spencer-nazism