I could be wrong but while Disney own the rights to most of Marvel universe these days I'm pretty sure it's Sony that owns the rights to the Spider-Man franchise. Hence it makes sense for them to secure an exclusive of their own property. Unless Disbey bought Spider-Man recently?
Sony only owns the film rights. Everything else(merchandising, comics, games, tv, etc) belongs to Disney.
I think Sony was pushing them, as Disney/Marvel was absent in console gaming lately, so that they could make the games instead of Activision (which were mostly movie tie-ins)