According to what is actually said in Bloodlines, vampires' internal organs are all atrophied, so there's no reason. But it's Nines Rodriguez, man. He's cool. And that's why. It's just a game, you know? Aside from that, Jack does make it clear that bullets do hurt vampires, it just takes more to kill them. It's not enough to just nick the heart, or anything like that. It's conceivable that Nines severed the spinal cord of the other guy, or something like that. I imagine that would hurt. I wouldn't think too hard about it, though. Not that I expect you not to.
Have you played it before, though? If not, first: I hope you patched it with either the True or Unofficial patch. It's basically unplayable without them. With them ( I've only ever used the Unofficial patch ), it's ... easily one of my favorite games ever.
Secondly, well ... enjoy!
Edit: Also, to the other suggestions ... Masquerade's vampires aren't really vulnerable to garlic. Staking doesn't kill them ( just paralyzes them ). Crucifixes aren't dangerous by themselves, either, as I understand it. Strong faith can repel vampires, however.