I guess my definition would be 1:1 to this one:
@orb85750
Philosophical Perspective (what you asked for):
The API is what defines something Amiga, because everything else (the entire "environment", all the underlying OS code (all the libraries, devices, etc)) derives from that, as well as all third party applications that makes use of it. The API is the core, it's what sets the rules, the possibilities, the limitations, and everything else comes from this. Hence, anything that can put up a proper Amiga API is Amiga, including (in order of appearance) Amiga OS 1-3, AROS, MorphOS and OS4.