Really, the player’s role in the game narrative is very similar to how the Outsider must see things:
First of all we are outsiders to the game’s world. Its rules and limitations are meaningless for us.
Then we get to control the two playable characters almost at the same time the Outsider appears/reappears in their lives. We start to control them, to make choices for them, to choose their powers and behavior, often depending on our knowledge of character’s possible futures. We see the world from the eyes of the protagonists, but we do not understand them fully – we do not know their pasts, their thoughts and even their motivations sometimes.
Plus we also are there for fun. We play, because we find it interesting.
The Outsider’s dikeish demeanor is very recognizable in the Internet’s collective unconscious. If you got a bunch of gamers decide on some character’s fate, said character would probably end up terribly broken, conflicted and mentally damaged.
We, players, give to the characters the ultimate power – the power of multiple tries (save-load). When Corvo meets Daud, he wins, no matter how good Daud is – because Corvo is favored by the Outsider in-game and because we can try as long as we need outside of the game world. Granny Rags too is unkillable until we burn her cameo – so those, who are on the good side of the Outsider, do really have more than one “life”.
I do not think, of course, that my idea is consistent with the lore or even sane, but I’ve thought that it’s an interesting interpretation.