I took this as meaning that the loop started again. I'm of the opinion that the events at the end of the game were only for the player-slash-the-booker-the-player-was-playing-as's benefit. It's impossible to make any sense of the them otherwise. The only other explanation is that it's an accidental plot hole - which I doubt given the amount of work that went into this game.
The Booker you were was not the Booker that could have made the choice at the baptism, his shot at that choice had already been made. The whole ending has to be for his edification, it's Elizabeth filling in the blanks for him, showing him what he had done. Otherwise there should have been two Bookers in every instance of those events (the baptism, giving away Anna, chasing down Constock to try and get Anna back, etc.) The Booker you played as was completely out of the time loop for those events, he was from 20 years AFTER he had already given away Anna, those choices were just simply not his to make. It was a farce. Elizabeth loved him, but she also detested him for straight up selling and abandoning her (remember how violently she reacted when she thought her mother had done the same). She put down that version of him peacefully, like a puppy. Drowning that version of him made no difference to the timeline, it was just to bring closure to the story of her Booker. Don't forget at least a dozen of him (probably many more) had already been set on that path and failed before you got there as the player.