Inter-operablility and interchangeability of parts means that it's possible to validate an implementation to at least some degree.

The best example that I can think of off the top of my head is the OpenGL 4.4/4.5 work that is nearing conformance for the Mesa3D project ( https://en.wikipedia.org/wiki/Mesa_(computer_graphics) ); while the functional coverage for the main modern drivers is 'complete' the official conformance testing has already resulted in some bug fixes and additional areas to focus on improving.

That real life case study is yet another example of how an API and conformance tests built around that API result in better code and in a more consistent experience that isn't dependent upon a mono-culture implementation.

If not an "Application Programming Interface", isn't all code an Interface? There's input and there's output.

With Object Oriented programming, that there is an interface is more explicit (even if all you're doing is implementing objects that are already tested). There are function call argument (type) specifications (interfaces) whether it's functional or OO.