It is not just the self insert, although you admit your choices is based around what you want to see, because you know, that you can roll back and see an another version of it.
.
In the other mediums, You are purely a
Watcher. nothing more. yet, You will developing feelings. You gonna be more interested in one aspect than the other. You may dislike a character more then an another, or a certian storyline. But you don't have
influence over it no matter What.
In a Video game, You are not just a Watcher, You get the change to shape and influence the things for your own liking, In what kind of extend you get the chance to shape the things depend on the game.
Even if you dont do it as deep as some kind of Role-playing. Your choices will be your choices, based on your own feelings or likes.
That's the difference.
And surely there was movies, or tv shows, or even books, where you would like if a certain character would be removed, or getting less screen time, or the generality that if it was up to you you would like it to be diferent, or simply you would just like it better that way.
No other medium allow you this, except Video Games.