I find the Lutece's mention of Booker not rowing, the coin flip ... As an interesting way to break the fourth wall. The big Bioshock reveal got me thinking about it years ago. In my mind - Andrew Ryan's speech and the Lutece's actions - is a neat way to provide a sort-of meta-commentary about games and the people that play them.
Like Elizabeth said, there are multiple doors, multiple cities, multiple stories being told all at the same time. As a gamer, we are those stories. I opened one door when I played the game, as did everyone else who played and finished the game. Yet, as Elizabeth goes on to mention, there's ultimately one way for the story to end - one way for the game to end - and in that we don't have a choice. The player doesn't have a choice.
At the end of the day - We're the constant - the player is the constant. How we interact with the game and the memories we develop through the course of playing the game, those are the variables.