Simply put. It's a computer that runs AmigaOS natively.
Without the Amiga operating system there would be no Amiga computer :-)
I agree with Fishy_Fiz and Drummerboy above, and would like to add on top of their comments: Back in the days, when the A500 was at its peak and was mostly used for gaming by the broad groups of users, the OS was at best very far, far in the background. The OS never had a focus or a priority in development back then, not even from Commodore. Often you used kickstart to physically bring up the computer and loading a game, that then took over and had its own ways of utilizing the Amiga HW directly. No sight of what you would call "AmigaOS" today, and by your definition, an Amiga 500 playing a game won't be an Amiga!
I have full respect for people thinking Amiga is all about the Amiga hardware. Because they are right; traditionally, Amiga was always about the hardware, and the OS was secondary and nothing that was really developed and evolved in a way even close to the HW evolution.
I think what you *really* want to say, however, was something along the lines of "It's all about the API" that I wrote in my comment above. I think this is what you really wanted to say, -Can it run an OS that behaves the Amiga way, has the Amiga strengths and weaknesses, the Amiga ways of doing things, runs the Amiga appliactions, etc, then it's an Amiga. But then you realized that this would also include AROS and MorphOS in the philosophical definition of what Amiga is, and because of that, you also choose to combine it with the Trade Mark definition, in order to exclude the others. "Only AmigaOS(TM) is Amiga". I'm not surprised with that, coming from you, but it's sad to this kind of apartheid mentality everytime it shows...
