Only because there’s a handful of movie producers that keep making movies from her books. Mostly bad movies, and still not nearly as many as have been made from King’s books over the same time period (oddly enough also mostly bad movies). But for good or ill King is a much bigger part of modern culture than Austen, because he’s more read, and movies made from his stuff are more watched. He might not be as good a writer as Austen (although frankly I couldn’t even finish the cliff notes of Pride and Prejudice, quite simply the most painfully boring book I’ve ever put in front of my face), but he is more a part of our shared culture.
First of all there’s more of King to adapt compared to Austen’s six complete novels. Second of all it’s not just the straight adaptations of Austen but stuff like Clueless, Bridget Jones’s Diary and ‘Bride and Prejudice’ and something currently in rpoduction called “Jane Austen Handheld”. Not to mention literary take offs like the recent “Pride and Prejudice and Zombies”. I would say that in the last 15 years more people have seen stuff based on her work than King’s. There is a veritable Jane Austen industry with tons of supplementary material on prominent display in bookstores.