Lucas was wary of that label because science fiction had a (well-earned) reputation at that time as a ghetto of heavy-handed allegory with hammy acting and terrible special effects. Lucas was striving for more than that.
He was trying to create a modern myth, or modern fairy tale. But genres are defined by their conventions, and Lucas chose space opera conventions (space ships, lasers, aliens). Space opera is a subgenre of science fiction so Star Wars was considered science fiction.
J.R.R. Tolkien was like Lucas in that he also tried to create a modern fairy tale. But he chose wizards and dragons, so his stories became fantasy.
Any fantasy movie in a futuristic setting (even one that's technically in the past, like Star Wars) would be widely considered science fiction. Granted, that is a common definition of science fiction.
But science fiction can also be something like The Twilight Zone: a genre that explores "what-if" scenarios. A genre that takes some fictional premise and attempts to explore the consequences logically. An example premise could be, how might modern society have evolved if the Greek gods were real? A sci-fi story would try to approach that question in a scientific and logical way. Star Trek often followed this pattern. Star Wars doesn't.
A weakness of defining sci-fi by a futuristic setting is that you can change the genre with only superficial changes to the story. Other major genres - comedy, horror, mystery, romance, action - are defined by the feeling or thought process they try to evoke. But take Star Wars and replace the planets with kingdoms, the Jedi with wizards, and the force with.. well, that's fine as it is.. and you can create a story with the exact same plot points but without a futuristic setting. There's no actual science in Star Wars; only a futuristic setting.
Setting doesn't feel like it should be the feature that defines a genre. You should be able to have a comedy, horror or mystery take place in a futuristic setting and a sci-fi that takes place in the present (and we often do, eg, The Handmaid's Tale).
I'll note that there aren't many movies that stick to just sci-fi; most incorporate a lot of action (like The Matrix). This is probably because filmmakers feel 2+ hours of science fiction would be boring. The movie The Martian heavily cut from the science of the book and focused on the action (while the book had little action and a lot of science). You see a strong sci-fi focus more often in literature and TV.
I don't know if Arrival has a book, and if it does I didn't read it. But the movie seems pretty solidly in what you're describing as "sci-fi" here. Takes a single premise and then builds the world around that "what-if". Same with Contact and Jurassic Park, with touches of drama and action / horror, respectively.
Yeah, Arrival fits well and I enjoyed it. There are a number of lower budget films you could add to that list like Primer, Moon (2009), or Gattaca. Ex Machina is sci-fi + drama. I'm sure there's plenty more. There's just a tendency for sci-fi films to lean heavily into action (or occasionally horror) like The Martian film did when compared with the book.
Jurassic Park feels more action/horror focused to me, but it has a sci-fi premise.
https://youtu.be/0qxcEBI1iKI
They both call it science fiction.
Lucas was wary of that label because science fiction had a (well-earned) reputation at that time as a ghetto of heavy-handed allegory with hammy acting and terrible special effects. Lucas was striving for more than that.
He was trying to create a modern myth, or modern fairy tale. But genres are defined by their conventions, and Lucas chose space opera conventions (space ships, lasers, aliens). Space opera is a subgenre of science fiction so Star Wars was considered science fiction.
J.R.R. Tolkien was like Lucas in that he also tried to create a modern fairy tale. But he chose wizards and dragons, so his stories became fantasy.