They own the rights to the movies. They negotiated this with Marvel because both companies are shitbags.
To add on here, Marvel Ultimate Alliance 3 came out AFTER the PS4 Spider-Man game and has Spider-Man in it so there's clearly no exclusive license with Sony and Spider-Man videogames. They're allowed to make their own series but they don't have exclusive rights. No this, this is just the same bullshit Sony and Microsoft have been doing for years now. It's dumb and everyone hates it. I get really annoyed when I keep seeing people half way excusing it with things like "well they do OWN the character" which is definitely not the case at all.