Neoreaction is an intellectual tradition of right-wing political philosophy composed of bloggers who are ideologically descended from the ideas of Curtis Yarvin, better known as Mencius Moldbug. If you want the five-minute version, read Konkvistador's summaries. If you are willing to read a much longer introduction, try one of these. Or just read the Neoreactionary Canon, which includes all three.

Anyway, the relevance to the grandparent is that LessWrong has a non-trivial neoreactionary minority (3% as of the last survey), and that former SIAI employee Michael Anissimov and his friends went and made a neoreactionary website called MoreRight (an obvious pun on LessWrong). Eliezer Yudkowsky was not amused.

It's what happens when you look at the lessons of "Politics is the Mind-Killer" and "Reversed stupidity is not intelligence", and decide to ignore them because affective spirals are too much fun to give up.

But it's difficult to choose whether the correct reversed stupidity in politics should actually be libertarianism or monarchy. The former seems more popular among LW crowd, but that also makes it kinda boring; the latter seems more original, but is usually defended by worse arguments. So you invent a libertarian-ish monarchy world, where the freely competing subjects are not the puny average humans, but the Gods-Emperors of different states. (You call all other regimes "demotist" to show that they are actually all the same.)

Of course, putting it this way is not attractive, so you have to hide it in hundreds of pages written in obscurantist language, so that no outsider is really sure what you are actually talking about. Then you insert some interesting historical facts, and a lot of criticism of political left, some of which is insightful.

And then you keep promoting the new teaching in LessWrong debates, because clever contrarianism is your selling point, and LessWrong has a weakness for clever contrarians. And then you use your presence at LessWrong as a proof that rational people support you, despite the fact that your fans are actually a tiny minority here (probably even smaller than religious people; and LW is explicitly atheistic).

Better analysis can be found here: "Reactionary Philosophy In An Enormous, Planet-Sized Nutshell", "The Anti-Reactionary FAQ". The first article explains the ideas better than the original sources, and the second article shows that this map doesn't fit the territory.

EDIT: Ignoring the beliefs and focusing only on behavior, Neoreaction is LessWrong's creepy stalker.