Short form: No, this isn't too broad (as long as your Storyteller agrees), but there's going to have to be a significant gain in order to regain Willpower.
Long form: In order to get a real feel for how often this is supposed to apply, it's instructive to compare it to the other vices.
An obvious comparison is Greed.
Your character regains one Willpower point whenever he acquires something at the expense of another. Gaining it must come at some potential risk (of assault, arrest or simple loss of peer respect).
So: the condition is extremely easy to fulfill. (Pickpocketing a single coin counts. Heck, pickpocketing a tissue counts, as long as you value tissues.) But you don't get the willpower unless you risked to achieve it - so it's a meaningful achievement for your character.
Likewise, Gluttony is ridiculously easy to indulge. But it doesn't gain you willpower unless it causes risk to you or a loved one.
So, a similar balance applies to Envy. The key word in that description isn't rival, it's "important". It doesn't really have to be limited by how hard it is to find rivals; it's limited by how hard it is to gain important things from them.
(The reason that this vice doesn't have the "there must be risk" limit of the others is that there's no need. If you take important things from people, or harm them, the risk will turn out to be there...)
So you're correct, the 'rival' is not an antagonist. (An enemy may count as a rival, but only if they're in some way on your level, competing on the playing field you care about.) A brother, PC, authority figure, rich white banker... all fine targets, as long as you distinguish between Envy and the other vices. Stealing indiscriminately from rich people fulfils this vice just fine, as long as you play into the spite of it. (For your character, the benefit isn't just the theft, it's that your gain is stealing from those rich bastards who didn't deserve what they had. Maybe they'll appreciate money properly now you've emptied their accounts.) You don't need to worry about the balance, because you don't get the willpower unless you've done real damage... which isn't easy and is bound to have it's own consequences.
(Failing that, apply player rule 0: Push it until it cracks; trust the GM to to rein you in.)