Ending - Why does this happen to Booker?

Spoilers ahead: Read at your own risk

I know that DeWitt and Comstock are two incarnations of the same person in different universes. With that, why does Elizabeth kill The player at the end? It has already been shown previously with the Lutece twins that killing someone in one universe does not affect their fate in another. Even if if did, Comstock is already dead and even though they spoke of it, they never killed the baby. They killed Booker as a grown man after he/Comstock had already done the deed.