For me, Amber is one of the prototypes of the concept "roleplaying game" in my head. That's part of the frustration of this argument, is that I, as I suspect the vast majority of people do, have a prototype-based idea of what a roleplaying game is; for me, an RPG is something that is like D&D or GURPS or Amber, though that's making explicit what's implicit, and not nearly so simple or limited. Aggressive declaration that these things aren't RPGs is frustrating, because it's simply outside the bounds of discussion; this things are RPGs, the question is does the definition cover them.
Again, as I said I am fuzzy about whether Amber is an RPG or a story game, and I'd be happily convinced either way.
I think it is safe to say that neither you nor I know the definition of an RPG. All we can do is make lists of things we think are RPGs, and things we think are not RPGs. Our lists will probably not match up exactly. After that we can only try to explain why we think that this or that belongs on the list.
"Whose Line is it Anyway" is one of my opening examples. I declare that the games played on "Whose Line is it Anyway" are not RPGs. I do not think that it would occur to anyone to list them as RPGs or to say of them naturally that they were playing RPGs. While there is a theoretical connection to Dungeons and Dragons, I think it is safe to say that the sort of play that always occurs in Dungeons and Dragons need not and might never occur in WLiiA, and conversely the sort of play that always occurs in the theater games on WLiiA need not and might not ever occur in Dungeons and Dragons. With me so far?
As a side note to this, whatever our definition of RPG is, it has to include Dungeons and Dragons as the first and archetypal example. If our definition doesn't do that, then I suggest that the definition might define something, but its appropriation of the term RPG is inappropriate. In fact, I believe that Wick was actually offering a definition of "story game" and incorrectly labeled his definition RPG. One reason I believe that is I'm inclined to think that the theater games in "Whose Line is it Anyway" do fit under Wick's definition, and do exclude Dungeons & Dragons. Wick declaring his preference for story games over RPGs is perfectly acceptable, and had he done so, I think he would have provoked a bit less nerd rage (not that anything fails to provoke at least a little nerd rage). But by misusing the term RPG to apply it to a story game, he confused himself and his readers.
(Which is not meant personally: I can certainly discuss the categorization without rancor. I can understand that Celebrim's definition of RPG may not include Amber. It's the dogmatic assertion of a definition that doesn't fit the prototypes in my head that's frustrating.)
I'm not even asserting I have the definition of an RPG. I'm not sure a really definitive and useful definition exists. All I'm trying to do is show why I think Amber might be outside of it by noting that in my limited experience with it, it shared with theater games a need to resolve action by appealing to the narrative preferences of the players and not by appealing to the rules. The lack of a fortune mechanic and the consequent lack of any unknown quality, the sort of arbitrariness involved in deciding how to apply mechanics, the dramatic empowerment of the gamemaster to just decide the outcome without recourse, all struck me as being very much an elaborate theater game. I think that I'm prepared to suggest that any game without a fortune mechanic is not an RPG because its that fortune mechanic that critically ensures the potential for failure and weakness of all the players, but I'd love to hear your take on it.
I think my definition would be something like:
a) Is there a fiction that is important to the resolution? (Chess: no, no one need really think of the game as representing a battlefield)
b) Are you playing a role? (Chess: no, you are directing a large number of pieces, none of which you are required to identify as you)
c) Is there a fortune mechanic, such that you can offer propositions within the fiction without certainty of success? (Chess: Hmmm... Taken as a whole the game itself could be taken as a fortune mechanic, weighted so that it was more likely that the player of greater skill would win, but on the whole, no.)
Now, by this definition, what would it take to make chess a RPG?
a) There would need to be a fiction, what some have helpfully called "the game board". Chess's existing game board is not a fiction, but it would be easy to imagine chess played on a game board that was a fiction - having multiple perhaps connectable boards and some sort of 'fog of war' mechanic so that you never knew exactly what would be on the next board.
b) Each player would need to play a single role: That's fairly easy. We just distribute a knight, bishop, castle, or some sort of balanced fairy piece to each player.
c) There would need to be fortune mechanics.: Again, that would be fairly easy. We could just assign a random chance of succeeding at capturing or resisting capture to all the pieces. Obviously, some work would be required to actually make this interesting and not merely a game of random chance, perhaps by giving each piece the ability to absorb hits or having a chance of pulling off some sort of fairy alternate move (knights stretching to move an extra space, castles bowling over two pieces at once, bishops shifting to an adjacent color, etc).
I assert, at that point, chess is an RPG. And I think critically, it meets H&W's definition as well.
UPDATE: It just occurred to me that if you only have 'a' and 'c', then what you have is a wargame. And it is precisely the invention of 'b' in the context of a wargame that is credited with the invention of the RPG.