It was the events of Eric (and the end of Sourcery) that resulted in Rincewind's Immortality and temperment.
Rincewind was cast into and STUCK in the Dungeon Dimensions
and then by freak accident summoned and reversed summoned through a Summoning Ritual
that gave him demonic powers. Hence, his extreme Post Traumatic Stress Disorder that he is known for is first seen in this book; and the details of the summoning combined with having been Place Beyond Time
when Discworld was created changed his metaphysical state.
Eric returned home at the end.
- If Rincewind ended up back in Ankh-Morpork, then Eric must have made it out safe too! Whether or not he practices demonology remains a mystery.
- Probably not, given that he isn't heard of later.