The way I think about it is, an RPG, or more specifically a CRPG, is effectively a self-contained alternate world governed by a universal ruleset, whose goal is, on a broad level, there to explain the rules of reality in an abstract and easy-to-understand fashion that we can relate to our own perceptions of the world. That's a really overwrought way of saying "this game has turn-based combat and stats because it's an easy way to quantify and express what are extremely complex temporal, spatial, physical and cognitive relationships."
The role-playing we do in CRPGs is something that should be, at some level, reinforced by the ruleset which governs the world. Whether that's something as simple as requiring a Charisma of X to persuade Y, or more intense patterns of interaction (individual NPCs remembering prior events and responding to them in believable ways), my self-assigned role exists within the game as a collection of statistics, variables and choices - with the reasoning for all those decisions sitting at the other end of the computer screen. In a sense you can think of the mechanics as the "game" and the player as the "imagination" draped over top. We can have fun with a game on a purely mechanical level, and indeed it's arguably necessary to enjoy a game on any more than superficial levels... but it's the player's imagination, as recursively structured by and influencing the game underneath, that provides much of the vibrance that we ascribe to the CRPG genre.
Perhaps it's just me, but that's why I've never been able to fully enjoy CRPGs that rely entirely on mechanics to carry them forward - I can appreciate a game whose mechanics are solid and well-designed, but I need an interesting layer on top of it, something that stimulates my own creativity and responds to it, in order to have fun and to keep me interested and engaged for the long haul. On a broader level I think this is true of all videogames, but CRPGs are one of the few genres that are more closely centred around this dynamic. A shooter, for instance, can possess both these qualities, but a shooter also doesn't need a great story, characters or visual design to capture the imagination and the senses - those things are nice to have, but they aren't a core aspect of my enjoyment of the game, only icing on the cake, as it were. With a CRPG, my influence over the game world, illusory though it may be, utterly demands that I be emotionally and intellectually invested.
Ultimately, the best CRPGs shouldn't rely on self-imposed roles and acting - I shouldn't be sitting there thinking "oh, I've got to eat now, because it's dinner-time in the game and my character should probably have food", or "well, my character is a smooth talker, so I should use diplomacy to get through this situation", at least not explicitly. Role-playing without the numbers, the mechanics behind it, is empty and unfulfilling. The best CRPGs are the ones which provide all the incentive you need to adhere to a role, to inspire you to aspire to it - entirely through the mechanics they provide, and in a way that anticipates the player's response to continue feeding him or her.
