In my opinion photography is close but still distinct enough that I would call it separate from art, film takes this even furthur. Cooking is way different from art, sure you can add the word "arts" after anything, but all it's really saying is that the thing is being done in a creative manner...
I don't think I've ever heard such a circumscribed definition of art before. Did you get this conception of art from somewhere or is it just a personal redefinition of the word?
You don't count film or photography? What about art that targets other senses besides vision like music or culinary arts?