I'm not very familiar with this specific fanfic. However, generally, a fanfic about Loki and Thor might explore their complex relationship in the context of the Marvel universe. If Loki is intersex in this fanfic, it could add an interesting layer to the character's identity and how they interact with Thor.
His character could also develop in terms of his powers. Maybe the abandonment was related to his latent magical abilities. He could start exploring and mastering his powers more in the fanfic. Thor's presence could either be a hindrance or a help. If it's a help, Thor could encourage Loki to use his powers for good, which would be a big step in Loki's character development.
Thor could be the one to help. Despite their differences, Thor is his brother and would notice Loki's ailment. He might bring Loki some sort of Asgardian remedy or just stay by his side to make sure he's okay. Another possibility is Heimdall. With his all - seeing abilities, he could detect Loki's sickness and offer his assistance, perhaps guiding Loki to a place where he can be healed.
Perhaps Loki is forced to stay in Jotunheim. There could be a powerful spell or curse that binds him to the realm. This could lead to an interesting plot where Thor has to find a way to break the spell and rescue Loki. It would also give Loki a chance to explore his identity while being stuck there.
One common theme could be redemption. After experiencing abuse, Loki might be on a journey to redeem himself or find a way to heal. Another theme could be power dynamics. The abuse might be related to power imbalances between Loki and Thor, which can be explored in different ways. And also, the theme of forgiveness could play a role, either Loki seeking forgiveness from Thor or vice versa.
Well, it can be a way to bring more diversity to the fanfic world. It allows fans to explore different aspects of Loki's character that might not be explored in the official Marvel stories.
Loki is not typically shown as gay in the main comic continuity. But comics are diverse, and there might be rare instances or special editions where his sexuality is portrayed differently.