I'm sure there are those out there, like myself, who would enjoy reading a fanfic based on actual characters that exist and actual events that occur in the game. However, I feel that I should warn you that sticking too close to the gameplay might not be easily embraced.
My own fanfic begins just as the game does, with my main character being carted off to be executed in Helgen. Though I had planned my Dragonborn's story and interactions with other characters to go well off-course of the main and civil war questlines, I wanted the opening scenes in Helgen to follow the gameplay closely, because that is the one part of the entire game that is the same for everyone; it's as close as we can get to canon in a game whose outcome is entirely determined by the person playing it, and I didn't want to mess with that. Unfortunately, this choice was met with some criticism. Readers did not seem to enjoy reading a scene that they had already played through numerous times, and I suppose I can't blame them for that. But I have to wonder how many people stopped reading after or during that first scene, judging the story as too close to the gameplay, instead of giving the rest of it a chance.
I ended up revising my first chapter to remove some of the game dialogue from the Helgen scenes, and to streamline a lot of the action in those scenes as well, since, from a storytelling perspective, they didn't really fit, anyway (e.g. going through four or five battles in the underground tutorial sequence). However, I was determined not to completely compromise what I wanted to do with those first scenes - follow the canon of the game, and start the story where it starts in the game - in order to appease popular demand, and so my first chapter still deals with my main character escaping execution in Helgen and proceeding to Riverwood and Whiterun.
I'm certainly not here to tell you what to write or what not to write, because I believe a writer should write whatever they want to write! But I wanted to share my own experience with writing a fanfic based on gameplay. Hopefully it will help.