@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.
Rhetorical Perspective (is there *really* any doubt that the Amiga was a series of computers made by Commodore that died in 1995?):
The Commodore Amiga 1000-4000 (and anything in between) HW, coupled with Amiga OS 1.0-3.1.
Trade-Mark Perspective (what unfortunately seems to be the most important thing to way too many people around here):
Anything that has a valid Amiga trade mark, properly licensed (or kind of "robbed" like in Hyperion's case) from the legit Amiga IP Holder, including products from Hyperion, Commodore-USA, IContain, etc...