In no universe does it promote innovation, it stifles it actually and thats been show time and time again. Since you appear to not understand what a patent troll is (I'm not being snarky I can tell by your post) I'll explain. They do not invent anything, they are not creators, they are just a bunch of rich people who buy up vague patents and then use those patents to sue people actually creating things.
With all due respect, I have a pretty good understanding of NPEs, having evaluated many potential transactions with or involving NPEs. (NPE is the industry term of art for patent trolls.) Your explanation does not actually rebut my comment.
Whom do you think NPEs buy their patents from? Inventors. Why do you think inventors are selling their patents to NPEs? Because they've determined it's the best way to monetize their patents (one reason for that might be because the NPE, unlike an individual inventor, has much more negotiating power because it has the resources to enforce its patents when they are infringed). How do you incentivize innovation? By allowing innovators to profit from their innovations.
Unlike NPEs, most inventors would have neither the wherewithal nor the resources to go up against an infringing party and ensure their property rights are respected. In many cases, based on my own experience, the inventors retain an economic interest in the patent (in part, this is for practical and somewhat cynical reasons, because juries are much more likely to be sympathetic to the plaintiff if the inventor participates in the trial).
You reference to "vague patents" is not actually a complaint about patent trolls because vague patents are not exclusive to patent trolls. Companies like Apple and Samsung hold vague patents too, and are not afraid to wield them to intimidate competitors. If you want to address the issue of vague patents, you should address your complaints to the USPTO (if you're in the US) or whatever is the governing body in your jurisdiction. The example in this article is very obviously a patent that was held up by the courts—you can assume that it was not so vague as to be struck down. Apple just thought they could get away with infringing it without compensating its owner.
"they are just a bunch of rich people who buy up vague patents and then use those patents to sue people actually creating things" - Sure, but I don't think that's necessarily a bad thing (for the reasons set out above). For what it's worth, big wealthy companies do this too, even with patents that they are not using.