I haven't got to play the game yet (waiting for the real version aka PC version) but watching trailers and screen shots I'm pretty sure that the setting of this game is not, at all, steam punk. Just as the first game and the abortion of a sequel weren't steam-punks. All of them are diesel punk, maybe they have a few steam punk elements but in overall, 1- 20th century settings in both continuities 2- Story of the first continuity lean towards a perfect diesel punk game. That's all.
While I think this is a really dumb thing to even discuss, you might be right about the first Bioshock because the city was established right around the time of WWII, but this is clearly Civil War, steam-engine-era tech being pushed further than possible in Infinite.
Personally I just think we need a generic "anachro-tech" label for this kind of stuff and stop trying to come up with so many sub-labels. I occasionally like it when people do this kind of thing creatively like Thief, Bioshock & Arcanum do, but I hate labels like steampunk and mosts things made to deliberately fit the label of steampunk are terrible (except Steamboy).
This sounds like fans of a subgenre at odds with mass marketing.
In short - they call it steampunk because its a term most people understand.
But doesn't make them any less wrong.
In fact steam or diesel punk is not only about settings, it's about the general theme of a story. If the story resembles pulp fictions, it's diesel punk, if it resembles mid to late 19th century sci-fis it's steam punk. The original Bioshock could have been published in a pulp magazine, so it's definitely diesel-punk. Dunno about Infinite though.
First off, there is no meaningful distinction between diesel-punk and steam-punk.
However, that's largely irrelevant, as I'm just here to establish that, while Bioshock Infinite may be a very good game, calling it any kind of "punk" is fucking stupid. Bioshock Infinite is a big-budget piece of mainstream popular entertainment. Stop diluting punk.
[Bioshock 2]: the abortion of a sequel
You need to play more bad games, son. Bioshock 2 may have been an easy, thoughtless cash-in on a successful new IP, but it was the furthest thing from bad. In many respects, it even improved on the original 'prodigy' of a game in some really meaningful ways (the plot doesn't completely fall apart 3/5ths into the game, for one; and it actually has an ending).
Steam Punk <-- Wild Wild West <-- Will Smith <-- Kevin Bacon <-- Val Kilmer <-- Val Venis <-- Saving Ryan's Privates <-- Saving Private Ryan <-- Vin Diesel <-- Diesel Punk --> CM Punk --> CM Burns --> Kevin Bacon --> Will Smith --> Wild Wild West ->> Steam Punk