Honestly makes sense. I thought when it first came out that Guwon would be the Sisyphus character because of the title and his position as the head figure of the hounds, and Sisyphus was a greedy ruler who dared to defy the will of the gods and cheat death. But he literally grabbed Jinwoo and jumped off the cliff to their death.
Jinwoo wants to both lead the people of the town but also care for Guwon. I don't know if there's anything else though that he is guilty of that makes him the real sisyphus character in the metaphor. But it will be interesting to see how it plays out, if we see a next life or if he truly survives the fall this time.

Legend says Sisyphus is punished in the underworld by the god Zeus, who forces him to roll a boulder up a hill for eternity. Every time he nears the top of the hill, the boulder rolls back down.