>* But in that case, why are instruction booklets copyrightable, but not software APIs?* //
The instructions themselves are not copyrightable only a specific presentation of those instructions.
So if I create a new recipe for a dish. You can include that recipe in your book but you can not include the specific presentation - so you should rewrite in your own words, not duplicate my layout, not copy my picture without permission, but you are free to recreate the recipe as it's a method of preparation rather than a form of presentation. Now arguably my layout of the dish could be copyright too so you may have to plate it differently.
The instructions themselves are not copyrightable only a specific presentation of those instructions.
So if I create a new recipe for a dish. You can include that recipe in your book but you can not include the specific presentation - so you should rewrite in your own words, not duplicate my layout, not copy my picture without permission, but you are free to recreate the recipe as it's a method of preparation rather than a form of presentation. Now arguably my layout of the dish could be copyright too so you may have to plate it differently.