So it looks like "Columbia" is the Rapture of the skies, and that is has something to do with racial purity ("Burden Not Columbia With Your Chaff"). So probable eugenics theme, which fits with the time period (unlike Bioshock 2). Also probable parallel to the Civil War, with Columbia seceding into a supra-nationalist enclave (not unlike the Enclave).
He doesn't call it prequel though and drew no narrative connections between the BioShocks we have played and the one his team is making. "I don't want to think about that," Levine said to me. "I don't think it's particularly constructive to have that conversation."
Good fucking luck, dude.
Could be neat, but gameplay-wise it sounds worryingly like a Bioshock Total Conversion Mod with extra bells and whistles. After the pretty dismal sequel (before that, even) I've been worried about the "CHA-CHING CHA-CHING" sound that no doubt sounded loud between the ears of the 2K brass who, if you remember, were in pretty dire financial straits around the time of the first Bioshock, looking for a buyer but possessed of too many expensive franchises (GTA and Bioshock, in particular) to find one. Bioshock 2 was a rush job with some pretty stupid ideas, where it actually had them.
Anyway, the 4 years of development time might not really be a smooth unbroken process. They could have gone through several revisions of the game or they may have started a different game before working on Infinite. Game development is littered with false starts and cancellations that fans never hear about. My hope is that they've used that time to fashion a new engine, because the version of UE3 they used for the first two had some major limitations.