I don't think it's wrong to still look forward to this, but when a game is labeled as '(Big name franchise) (Number or title)' and has absolutely no correlation with the game other than 'Not Big Daddies' and 'Not plasmids', it makes me question if the game isn't just an attempt to keep the company afloat.
But the game has the same spirit has Bioshock. Some examples of the parallels:
Big Daddies - Songbird and Heavy Hitters
Factions: Atlas (sorta) vs. Ryan - Vox Populi vs. Founders
Dystopic Cities: Rapture, a failed underwater paradise free from government control - Columbia, a failed flying city that was intended to show the world the innovative ideas the US had and what they had to offer
Protagonist: Jack - Booker (though he talks a lot more)
Moral Dillemas: Kill or Save Little Sister - Use or Not to Use Elizabeth's powers at the risk of her health and safety
Splicers - Citizens of Columbia
And I am missing a few, but the point is that even though it is not the same Bioshock, Infinite is still a Bioshock game.