It's supposed to be proof that the tomatoes were "vine ripened", instead of being picked green, but the definition is such that there only has to be some sign of color change when they're picked to be sold as "vine ripened", so they're generally still picked mostly green.
So yeah, pretty much a marketing gimmick, although not all that new. (it's probably been around for at least 5 years near me). If you want good tomatoes, you typically need to grow the yourself or go to a farmer's market. (or have a step father that grows way more tomatoes than he can deal with)
It's possible that leaving the vine attached might help protect them from moisture loss, but you can also just store the tomatoes upside down.