I may be wrong but I think that's not the view of the modern PL community. If your API talks about values, combinators, and has (implicit) laws about them then I would certainly consider that a language.
Maybe the view that APIs are little languages can be seen as the view of the postmodern PL community.
Since object orientation brought the possibility of adding little languages to the masses and a few decades later value objects and lambdas and generics where added to all OO languages, a postmodern view may be quite an applicable and useful perspective to deal with this question.
Since object orientation brought the possibility of adding little languages to the masses and a few decades later value objects and lambdas and generics where added to all OO languages, a postmodern view may be quite an applicable and useful perspective to deal with this question.