Choi Joohwan does not die during the ritual. He continues to live his human life in the modern world.King Lee Seon no longer exists as a wandering, vengeful ghost or demon. Because Joohwan relinquished his earthly ties and accepted him during the ritual, Lee Seon's spirit entered Joohwan’s body.Lee Seon now lives permanently inside Joohwan as his Momju-shin (몸주신)his personal guardian god. is a bittersweet "happy ending" because they didn't get to live as two normal, living boyfriends. Instead, they achieved an eternal spiritual marriage where the King finally belongs entirely to Chanseong, right there in the living world.
Update
Ja Chanseong said "your forgiveness lies with me". At this point, the king alr became a demon and Ja Chanseong had some unresolved resentment because the king had him killed by poison back then, so he chooses to accept the king and asks the king to accept him as he exorcises him as a shaman and have both their souls trapped in the shaman's tiger bells forever.
So what happened to the shaman and the king? Did they both perish?