I started writing fanfiction because I started reading it, and thought the same thing: "Why are people doing this?" And then...I found myself wanting to write, too.
Because when I play, say, Inquisition, I love the game. But I love more than just the game. I love the conversations I start imagining in my mind - the ones the characters don't say. I love the dialog options i didn't get to say. And I love the other possibilities. for example, I kept thinking, well, my other Trevelyan would have come along with this one, right? And they both might have lived, even if only this one got the mark. so add a few more OCs, add some romance and action and...suddenly i'm writing.
In short, I love playing video games. But as I play, I then want it to be like the novel that starts writing itself in my mind, so I start writing the novel, and then the next thing I know, hey, we're at 140k+ and still not slowing down.
TL;DR - Fanfic Happens. If you know how to stop a writer from writing, that's the better question.
(oh, and in there, somewhere, should be a HUGE thanks to bioware for such a fun world, characters, and such excellent source material and being so willing to let fans enjoy their worlds)