MysterD: But, to me - RPG's usually involve any of the 2 traits below or a combo of both:
1. Characters can level-up their stats, attributes, abilities, skills, and/or equipment a lot.
2. Decision-making and branching paths...with different results in all kinds of ways. The results cab differ in the actual quest-line's outcome; NPC's, the game-world and/or the locations being changes/removed/killed/acting different/whatever; and/or actual different final endings to the game.
Funny thing is, neither of those is a defining aspect of RPGs for me. 1 I see as irrelevant to genre classifications (with the only genre I can think of that would really require this would, oddly enough, be idle clickers), and 2 is more along the lines of what I'd see might align more closely with visual novels (at least more interactive ones) and/or adventure games.
dtgreene: I generally consider RPGs to be games where the success of an action is determined by the character's abilities, not the player's. The player's role, in such games, is relegated to telling each character in the party what to do, and then just watching as said actions are performed.
Leroux: Wouldn't that include games like point-and-click adventures and chess? Guybrush Threepwood is safe underwater because he can hold his breath for 10 minutes, while the player most likely can't; but the success of trying to pick something up depends on his ability to reach it. A chess figure can or can't reach a certain field due to its abilities, not the player's. The player just tells Guybrush or the chessfigure in a videogame what to do and then watches as said actions are performed.
I know what you mean, but I don't think your definition is sufficient to exclude these cases.
So, a character can hold their breath underwater for 10 minutes. When you go underwater, does a timer start at the 10 minute mark and count down, in real time, from there (with the character drowning at the 10 minute mark)? If so, then the player's abilities are relevant, so my definition would not include that case.
Chess is a different case. The abilities of the pieces don't affect the success of an action; rather, they affect whether the action can be performed at all. This sort of mechanic feels more like it belongs in a puzzle game. Maybe chess is a puzzle game? (One other piece of evidence that points toward chess being a puzzle game: Watch any serious game of standard chess between reasonably experienced human players. Notice how long it takes for each player to make a move?)
Leroux: In any case, my personal take on the definition is that there is no single trait that can define a game as RPG, it always has to be a combination of several. To the ones already mentioned by Cavalary, I would add for example, as typical but not necessarily essential: inventory management, choices & consequences, roleplaying a character (e.g. through individual character creation, exclusive dialogue choices or different use of skills to solve problems), experience points and option to influence which stats improve on level up etc.
Quest 64 really only has that last point; the option to influence which stats (or, rather, magic elements) improve on level up. (Well, it does have XP, but it's hidden and only affects your element growths; other stats grow through use, albeit in a deterministic manner (unlike, say, SaGa games).)
Leroux: And does it really matter, if you're having fun? It's only there to help you give an approximate short description when promoting a game or talking about it with others.
A game does not need to be an RPG to be fun. I'm having a lot of fun with Celeste (with a couple mods, neither of which add RPG elements to the game), for example.
Edit: I should also add another point: A game does not need to be fun to be an RPG. See Ultima 5 NES for an example of this.