Backhanded compliments I understand and agree - passive aggresive. A really poor sport.
Dismissing someone out of hand, no insult, no explanation, is passive aggressive? That I don't hold with. If someone is not worth my time then they're not worth the time it takes to tell them that, and I don't.
In the strictest terms, it's not passive aggressive. I'm using it as an analogy. If we really get down into transactional analysis or something similar, with pre-written behaviour scripts, there is an argument for it being a form of PA behaviour... but it's not really an important point.
This is about how we interact with people - so if you are sitting down at a table talking to someone, what happens is that you'll find a way to assert your dominance over them and their ideas. If they say something you don't like, it isn't just rational... the arrogance comes out in how you dismiss the other person. Not as a permanent thing, but in how you convey that dismissal.
It is effectively being a 'bad sport' - if two people are playing sports together, that kind of behaviour would be defined as 'bad sport'. It'd be like trash talking. Even from our perspective, trying to help the other person out turns into a "look at me go, I'm so good, you suck" attitude! Nevermind that the attitude that we are the 'better' one is arrogant to start with.
(Edit: Jennifer is correct, INTPs would fall under PA for sure... and INTJs do something similar, but I wouldn't call it PA. Either way, they both share the same dismissal, which is the core of being superior and therefore arrogant)