Wikipedia says
A superhero or superheroine is a stock character that typically possesses superpowers, abilities beyond those of ordinary people, and fits the role of the hero, typically using their powers to help the world become a better place, or dedicating themselves to protecting the public and fighting crime.
So yes, he is definitely dedicated to protecting the public, but it feels wrong to call him a super hero. What do you think?
The Marvel and DC universes have loads of people with abilities, yet we call them superheroes.
Yes, but they all have different abilities. or at the very least don’t have the same ones often. Captain America can’t turn into a giant green monster, and so on.
I’m not so sure the definition provided is sufficiently narrow, but Luke Skywalker specifically doesn’t fit into it as given.