I can actually talk about this a lot. Bioshock Infinite is interesting both from a story perspective, as well as an FPS perspective and gameplay design one.
The whole game is (spoilers) about fate and the few constants. In video games, the player is always controlling things from the head down. People may talk about "choices" and the like, but unless you're playing a tabletop game or something choices aren't actually real. What IS real is the actions that you do, so any game that goes "oooh choices and multiple endings" is not entirely telling the truth, as in most cases your choice doesn't really matter.
It was also a criticism of other games in the same genre. There's always a man, a gun, and an enemy, just like the game goes about lighthouses and stuff. The game was also criticizing how because the player must be able to DO things inherently prevents games from being introspective or smart on a certain level because, like Spec Ops, you HAVE to do the thing the game will inevitably criticize you for.
It's similar in a way to why, in the end of Telltale's TWD Season 1, the guy has to go "hey that's my stuff you stole a while ago" because otherwise there isn't a way to have the player be responsible for their decisions.
Links to where this is talked about in a greater manner:
Kevin Wong takes a closer look at Bioshock Infinite's themes and how they related to game narrative and the ludology-narratology debates of yore.
www.gamasutra.com
WATCH OUT FOR SPOILERS has become a familiar warning in discussions about Irrational's big game. THIS POST HAS SPOILERS, TOO.
venturebeat.com
A growing number of industry voices claim BioShock Infinite's extreme, gory violence hurts the game, but it's integral to the message Infinite wants to send.
venturebeat.com
It's a simple premise — a guy, a girl, a gun and a debt to repay — but in Bioshock Infinite it becomes a mind-bending story about politics, oppression, change and sacrifice. Set in a flying city.
www.npr.org
Like, I could go on and on about this, but the people above are able to elucidate it much better than I can.
[Also apologies for replying to an old post, I'm going through the thread.]
[Also feel free to rate this autistic, I'm very well aware. But I think I'm given somewhat of a pass considering it involves my job.]