I don’t really agree with the premise. The core logic of a program can (optionally) interact with humans and/or other systems. With neither, one is left with a “run to completion” program that typically transforms its OS supplied inputs into outputs.

A “user interface” is associated with human interaction, whereas an API is associated with interaction with other systems. That human interaction is in terms of the user of the program, not the producer.

That programmers are human, might mean that they need to program against an API, but surely that doesn’t mean that the term “user interface” should be extended to it?