I haven't read this specific 'Never Left Tatooine' fanfic in detail. But generally, an analysis could start with the plot. Maybe it focuses on a character who is stuck on Tatooine and how their life unfolds there. It could explore the local cultures, the unique landscapes, and the relationships the character forms within the Tatooine setting.
In this fanfic, it might be that Vader is on a secret mission to find Luke. He could be using his dark side powers to track Luke down. And Luke, being on Tatooine, is probably just living his normal life, not knowing that Vader is coming for him. The fanfic could then focus on their encounter, the emotions involved, and what it means for the Star Wars universe.
Obviously, Anakin would be the main character. His mother, Shmi, would also play a significant role. There could be his friends from the pod - racing days like Kitster. And perhaps some Tusken Raiders who might have a different relationship with Anakin since he stays on Tatooine. Maybe they would see him as a more permanent threat or, in an interesting turn, a potential ally in some local matters.
In this fanfic, Anakin could stay on Tatooine because he has a premonition of the dark side that awaits him if he leaves. So, he decides to stay and focus on bettering his home planet. He might use his natural piloting skills to start a small trading business, using his pod - racer as a start - up vehicle. This would keep him occupied and away from the events that lead him to the dark side in the original story.
One aspect that could make it special is the unique take on the Tatooine setting. Instead of the usual stories where characters leave Tatooine for grand adventures, this one keeps them there. It might offer a more in - depth look at the everyday life on the planet.
Well, perhaps Anakin would start by reforming the podracing scene. Since he was once a podracer himself, he could make it safer and more fair. He might also train a new generation of pilots. And he could use his influence to improve the living conditions of the slaves on Tatooine, maybe even free them all. This would completely change the social structure of the planet.
In the 'anakin never left tatooine fanfic', it could be that Anakin, staying on Tatooine, discovers ancient Force secrets hidden on the planet. These secrets could be related to an old Jedi or Sith presence long forgotten. He might use this knowledge to better the lives of the people on Tatooine. For example, he could use these newfound powers to improve the farming techniques or build better shelters. His story would be one of a local hero, using the Force for the good of his home planet rather than for galactic domination or the fight between the Jedi and Sith.
Well, if Darth Vader looks for Luke in Tatooine in fanfiction, it could be a really intense story. He might sense Luke's presence through the Force, but the Force can be tricky on Tatooine with all the sand and strange energy fields. He could end up in a wild goose chase, following false leads. And who knows, he might even have to deal with some of the local criminal elements who don't take kindly to a Sith Lord stomping around their territory.
The Hutts would likely oppose Anakin. They have long held power on Tatooine through illegal and immoral means, and Anakin's takeover would threaten their control over the planet's criminal underworld and trade routes.