ESSAY WARNING!!!

sisyphus was punished for cheating death (and for being a poor ruler/betraying zeus) by being made to push a boulder up a mountain for all eternity, only for it to roll back down over and over again. it's representative of an exhausting and ultimately pointless task.

it's clear that gyuwon is meant to parallel sisyphus, given he is the "ruler" of the town and the hounds are his. his "boulder," his futile "task" is to maintain his power over/protect the town and keep ahold of jinwoo. im assuming his "boulder" rolls down the hill everytime he is betrayed and loses both the town and jinwoo, restarting the cycle (rolling back time) with his and jinwoo's deaths. I think they must specifically die falling off the mountain in order to be "reset." so i believe gyuwon makes the same request to die watching the town, and i think jinwoo chooses to grant his dying wish in every cycle, hence why they die the same way every time.

i think jinwoo parallels sisyphus as well. in his case, i think his "task" is freeing the town and freeing himself of gyuwon, which ultimately proves meaningless everytime gyuwon kills him. perhaps gyuwon himself is a representation of jinwoo's "boulder," as the framing of him "pushing" gyuwon up the mountain seems pretty intentional, and every time gyuwon dies + takes jinwoo with him, they're falling off the mountain and "rolling back" time, making everything they both did before that ultimately pointless/futile. i say they must be rolling back time because the town would definitely know something was up if jinwoo and gyuwon kept coming back to life without a time reset for all of them.

ultimately, they are the cause of each other's "boulders" rolling back down the hill.

assuming their deaths do result in them going back to the beginning, the entire story we've seen has likely just been another push of the boulder up the hill before it falls back down (when gyuwon and jinwoo die) and they start pushing it (their respective boulders) up again. however, the fact jinwoo has survived this time probably means the cycle has been disrupted/changed.

my own prediction is that gyuwon still "reset" upon his death, but because jinwoo didnt die too, they will have never met on gyuwon's end. i think jinwoo will make his way back to the town, find that no one remembers him, and end up getting into some kind of trouble with this new gyuwon who doesn't technically know him. gyuwon might try to kill him, as sisyphus was known for killing travelers who passed by/through his kingdom and we've already seen how gyuwon treats outsiders. but i think that gyuwon will have some lingering feelings (maybe a sense of deja vu/recognition) that will cause him to keep jinwoo prisoner instead of killing him right away. shenanigans ensue from there. i think a sense of deja vu could also explain why jinwoo kept trying to kill gyuwon, like his subconscious knows what's going to happen and tries to prevent it, even if his conscious remains unaware.

but that's just my own interpretation and prediction.