The classy word in the title is coined by one Tommy P. Cowan in an article on the works of famous Scientologist, junkie and wife-killer William S. Burroughs, and he defines it thus:
Archontism is a current of thought grounded in a sort of “negative epistemology” that sees human existence as controlled by ‘archons,’ or agentified barriers built into the natural world in order to block the paths to psychic transcendence.This is a step up above normal "conspiracy theory" - that your life is fucked up by a hidden cabal of bad guys - in that the archons are, in the glorious phrasing of the Church of the SubGenius, "not even human [but] shambling, unbelievable, unmentionable, unthinkable THINGS". In the Western tradition, this is most commonly associated with Gnosticism, and certainly that's the main vibe which comes out of all those great "modern gnostic" artworks that came out of the late 90s: Dark City, The Matrix, The Invisibles.
An earlier example of this kind of fiction is The Mind Parasites by Colin
Wilson. Much like many of the works of one of Wilson's sources, Mr Racist Recluse of Providence, Mind Parasites is not well written, far from it, but interesting and fun because of the ideas it includes. Brief plot: a scientist discovers that some immaterial alien beasties are holding humanity's psychic evolution back and causing mass suicides. He defeats the beasties using only Husserl's phenomenology (!!!) which gives him spooky superpowers - telepathy, telekenesis and all-round super-geniusdom, which he can then teach to others.
It is not a coincidence that this book came out in 1967 at about the time the hippies started getting into Scientology, and those are about the kind of powers that LRH promised his fan club. Scientology is not strictly "archontic", because (to very briefly summarise) in their mythology, we weren't fucked up by monsters, we fucked ourselves up. But it appealed to people who read stories like The Mind Parasites and wanted to believe that kind of thing could actually happen.
This reminds me very strongly that JRR Tolkien converted CS Lewis back to Christianity (which he had rejected in reaction to his tight-ass Ulster Protestant upbringing) by telling him that the life of Jesus Christ was just like all those stories of sacrifice and redemption that he loved in mythology and legendry, only it really happened. The point of the story is that people will believe anything, and just because we want to believe doesn't make it true. That way lies a huge waste of time or becoming someone's puppet or slave. "We preferred to live in Ron's fantasy than boring reality" - some Sea Org veteran
As it happens, my working reality-tunnel is that the superstructure of the capitalist mode of production (or, indeed, all class societies) is the closest thing you can get to an actual "archontic system". I suppose it's fine to believe that all those stories are just metaphors for what you really believe in, like CS Lewis would argue that those dying-and-rising-god stories were planted by YHWH to get people ready for Jesus. So maybe all those people who think Marxism is Gnosticism with the serial numbers filed off were right. Only in practice can it be worked out which is the map, and which is the territory, because the people who confuse the two will probably end up believing something really stupid, like a shitposter on 8chan is a timetraveller.