Ahh, yes it does, hence they're still called a hero.
Traditionally-speaking, an anti-hero isn't necessarily a hero by default. The term refers to an individual that rejects heroic tendencies out of their placid, self-serving nature, or because they find the notion of heroism to be a fictitious or impractical one. In other words, they'll walk the lines of both hero and villain, graying the borders of both to better cater to their personality. Spawn's a good example, since he unintentionally performs a number of heroic actions, but through harsh and often borderline-villainous means.
But they don't have to be a hero in every case.
Hellsing's Alucard is an example of a villain who's bound to the leash of "good" forces against his will, and while he displays a number of sadistic and villainous tendencies, gradually reveals his more humane and noble characteristics through brief character exploration.
Anti-heroes can play at being either heroes or villains, but what makes them compelling and endlessly-entertaining is their potential to offer an interesting alternative to both.
I've also heard people say they feel that Vergil wants power because he believes his mother died because she was weak.
Personally I favor the former
Given the rest of his personality, and his absolute and undying contempt for all things weaker than him---
especially humans---I don't see how the former theory makes even remote sense to his character.
If you consider how he acts and the traits he displays throughout the actual game (and before anyone leaps forwards with the paper-thin defense of the manga's contradiction to his game portrayal, bear in mind that it was made well after
DMC3's release and by a completely different author, meaning that Vergil's so-called "guilt rooted from Eva's death" was never even an inkling in Bingo Morihashi's mind when he was writing the scenarios OR the script for
DMC3), then the second theory is the only one true to his character.
You'll have to excuse me if I don't buy the fictitious allusions some fans have made surrounding a certain quote Vergil makes in a laughable attempt to justify his otherwise-merciless behavior.
I found it on a Japanese art sight called pixiv. You'll find that Japan stands as the greatest provider of
Star Fox fan art nowadays, probably because most of the North American
Star Fox fan contributions tend to be bad furry art and straight-up yiff instead of anything remotely cool.