At this point, you may be thinking "Sure, Weltschmerz guy, but not every reactionary stooge is a committed accelerationist, and they don't all have a conscious, fleshed out understanding of this cyclical model of history." You would be correct.
Nonetheless, many of them still point to an idealized past (which could be the 1980s, the 1950s, 1776, 1492, prehistory, or any other past time), gripe about the corrupt present, and indulge in eliminationist fantasies about destroying (or at least subordinating) their enemies so that they can reclaim their rightful place at the top of the social order. So the model still applies.