I don't know if you can put a label on revenge movies. I think its just too primal to be politicized.
Generally, though, the right supports hierarchy- hopefully, a good hierarchy- and it's kind of a point in vigilante comics/ movies that the system, the hierarchy, does not work. If it did, the Punisher wouldn't exist.
A good example of a right wing movie where the hero is lawless would be Robin Hood- who steals, violates the law, and so forth, but in the end, King Richard returns from the Crusade and retakes his throne from the usurper, returning the hierarchy to its proper place. Presumably, Robin Hood is not ambushing King Richard's tax collectors after that.
In movies like Batman, its much less clear if the system is redeemable or not.