Except its a term used for games like overwatch.
Battleborn is its own unique thing and its false comparisons like you are making that have harmed its sales.
People think its like overwatch when it simply isn’t.
And no, hero doesn’t mean playable character, it means unique characters with distinct abilities, gameplay differences etc.
A hero shooter is a shooter whose playable roster is comprised of such characters, rather than a normal shooter where the characters are not distinct.
Moba rosters are comprised of heroes, and the reason battleborn should not be considered a hero shooter is because it has far more similarities to a Moba.
It is a genuinely new thing and would likely have been the beginnings of a new genre if not for that its likely not going to get enough exposure to be the success it needs to be to warrant a sequel or inspire others.
The scrolling got a bit annoying, however.