One wonders what overly-narrow definition of API you're stuck on.

I suspect you stopped reading at web services on your link, but API is indeed the correct word to describe a set of functions from a library (built-in or not). If you disagree perhaps you should share your preferred term here?

> The term API is often used to refer to web APIs, which allow communication between computers that are joined by the internet. There are also APIs for programming languages, software libraries, computer operating systems, and computer hardware.