Green Arrow and Hawkeye are Batman with the utility belt transferred to arrows. Both have taken on their fair share of aliens, gods and monsters.
Taking that gear and skill set to fight crime and forging different identity using a costume and code name is whats them superheroes.
Agree that Punisher isn't a superhero because anyone can pick up a gun. Disagree that costumes, code names, different identities are essential to being a superhero. And I would add that the skill set is usually alleged, frequently not even shown. Superheroes like Batman, Green Arrrow, Hawkeye and Black Widow routinely avoid the threat of being shot, usually without even a commonplace kevlar vest. That is a superpower, even if it isn't openly acknowledged. The so-called explanation of their superior skill is just, in the phrase upthread, an in-story conceit.