That's right. I've got overtext, b****!©
What did I just say?
I can see why you'd get confused. A lot of the thematic text is about the control of Columbia while Elisabeth and Booker is still there.
However, with timeline 1, they simply escape Columbia and leave it to it's own demise. Letting the Founders and the Vox fight over the remains.
With no Elisabeth nor Booker running around the board, the game gets shortened by 5 world event cards. Keep in mind that
Bioshock Infinite: The Siege of Columbia rulebook, page 16 wrote:
If a world event card is ever supposed to be drawn but there are no cards remaining in the world event deck, the game is over.
So the end of timeline 1 is simply thematic.
I don't believe I'm spoiling anything by saying that the other timeline cards end differently
I hope this makes more sense than the ending of the video game.