Right have their mythos, that's true. But the righter you go, the less this mythos are treated as dogma. Neoreactionaries take as the stariting point where ideals of egalitarianism was accepted and terms "Right" and "Left" appeared - those who did accept became "Left", those who not - are "Right".
Neoreactionaries are Right in this coordinate system, and from their viewpoints almost every living political discourse is on the Left side (with different degree of Leftiness, Fascism is also quite far left). It should be also noted that Neoreactionaries are not traditional Conservatives (who are drifiting to the Left as everyone else just with a generation or two lag). The biggest difference is probably that Left is too dogmatic: you have seen yourself - democracy does not work in Africa but instead of treating government system as a tool and changing it to work, Left apologists just call for another Revolution. Sweden evolved (or devolved) to totalitarian state etc. Neoreactionaries do not treat political theses as religious. The main point of divergence is that Neoreactionaries do not believe in equality and do not accept egalitarianism.
It is not something that this is something new, though. Ochlocracy - and modern "democracy" is step short from the "Maidan" - apotheosis of mob rule - was always considered a receipt for disaster. You can consider appearance of antiegalitarian discourse in Western thought as a reaction against horrors which mob rule inevitably brings. This is natural and you should not be afraid.
Indeed. EU is just a part of Europe, and only a period in time.