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

One wonders why you wonder.

https://en.wikipedia.org/wiki/API

Well, given this quote from your reference:

> The interface to a software library is one type of API. The API describes and prescribes the "expected behavior" (a specification) while the library is an "actual implementation" of this set of rules.

Yes, I still wonder why you'd be picking this particular silly semantic battle.

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.

> API is indeed the correct word to describe a set of functions from a library (built-in or not).

Uncorroborated by WP, note.

> If you disagree perhaps you should share your preferred term here?

Library functions.

“API” meant “library functions” long before the first web server responded with JSON.