The action, the intrigue, the everything of role-playing happens in one's mind. The abstraction of rolling dice to represent something happening in a shared imagined reality, the scribbling of a series of lines on graph paper to represent a location in which the PCs are exploring, speaking in funny voices, the naming of people that don't exist and aren't even present in the shared imagined reality...
The compilation of all of these disparate and nonsensical parts are assembled and turned into a cohesive thing by the imagination. And it's the same thing with books. Words and words that represent people that don't exist, places that don't exist, actions that never have and never will happen... assembled into a you-are-there history that's entirely made up.
The process of playing a role-playing game is the same process as reading a story. In a game, the false reality is created through negotiation and mutual agreement of factors that are imposed on that reality (the rules). In a book, this is all simply dictated by the author. The interactivity of the RPG offsets (and causes) the fact that a written story is going to be compositionally different than whatever happens in a gaming "story." Six on one hand, half a dozen on the other, and attempts to close that divide are doomed due to the inherent differences in the forms. The adventures of Dorf the midget warrior won't be as exciting as those of Conan to an outside observer, not by a long shot, and the end result won't resemble a good piece of fiction if written out in that form, but you did it, and you did it in a situation where there were an infinite amount of possible outcomes; you didn't just get told about it or follow along.
It's the same process. Words of a nonexistent, and in many ways nonsensical nature being accepted as happening within the mind's eye.
That part is clear to me. The following is a little less explored, but I figure I'll work it out easier with some comments...
Adding more sensory elements deactivates the imagination more and more. Radio plays pace you with indifference, whereas even a storyteller talking to you face-to-face will himself choose what is important even if he is using techniques to draw you further in and know when to draw something out or storm forward in the narrative. TV and movies give you everything - what the hero looks like, what the dragon looks like and how it moves, what the castle looks like, exactly how the one character's face twitches as he speaks... it's still a story and it can be enjoyed (and my sizable DVD collection will prove I don't say that condescendingly), but it activates the mind much less than does a written, or even spoken, story.
Enter gaming. Every visual element that is added disengages the imagination in some small way. What used to be abstracted and imagined is now detailed and quantified. Books often have maps and illustrations, as a picture is indeed worth a thousand words. So too do RPGs often have artwork to illustrate difficult-to-describe elements, such as a map or handouts and the like.
But when do such props stop enhancing and enabling the imagination and begin to replace it? Worse yet, when do such props and methods actively interfere with the imagination? I put forward that games which include minis (or any positional or literally representational markers) as part of the rules of the game are fundamentally and objectively lesser and less imaginative forms of role-playing. I believe the same of any game with a strong visual element (I can't think of any examples with audio elements offhand). They may still be enjoyable, but it is differently enjoyable the same way that movies are enjoyable differently than books.
(I do want to mention those TSR modules with the illustrations to show players - Tomb of Horrors, Expedition to the Barrier Peaks, Hidden Shrine of Tamoachan, do fall under this criticism, although I will also say that only a very few, and only one comes immediately to mind, of the included illustrations are necessary at all.)
This applies to MMORPG and 'virtual tabletops' as well. This does not include all of internet gaming, as play-by-post (even if it is slow to a game-killing degree in my estimation)/IM/Skype/etc gaming retains the core values of role-playing. It's the graphical representations and the standardization inherent in computer gaming presentations that kills the essence of role-playing. Again, not to say that they are unenjoyable, but it is unfortunate that they have been given the same "role-playing" label that Dungeons & Dragons and Runequest and Traveller use because they are not the same things.
The actions, the interactions, are less important to defining a role-playing game than the fact that it takes place in your mind. Whether our hobby, the traditional role-playing game hobby, is erroneously named, or whether its offshoots are wrongly labeled is unimportant (although I vote for them... RPGs didn't keep the 'wargame' label after all, even though that's where they came from), but the confusion causes more problems than it solves by enabling fan cross-pollinization.
I also believe that licensed properties, even those that exist purely in literal form, inherently create a conceptual limitation of imagination based on being attached to a particular already-extant idea. This holds to various degrees. I played a lot of TSR's Marvel Superheroes as a teenager, but never once used any actual Marvel characters nor set my games in the Marvel Universe, and I believe that my games benefited from those decisions. Call of Cthulhu masterfully overcomes its licensensical limitations by taking from an entire genre's literary inspiration (and publishing that inspiration, something TSR and D&D never did for fantasy) and not just Lovecraft's. But generally taking on the weight and canon of a licensed property heavily corrupts gameplay using that game, and always does if set in the actual setting that the game is supposed to be presenting.
Hell, one could say the same, and for the same reasons, for any setting of sufficient detail and have a valid argument, and certainly any with metaplot would provide an inescapable argument as the game designer is taking 'what happens' away from the game table altogether. Planescape and Ravenloft and Dark Sun were further liabilities of AD&D 2e, not its redeeming factors (due to excessive setting detail, not initial concepts, a problem that also infected the Realms).
It's the pastiche of particular literary influences in combination with an implied, rather than described, setting which unlocks the greater potential for a game. A series of works that are at the same time complimentary and similar, but also contradictory and inconsistent for one another, makes for a wonderful game as the individual group must make their own basic setting decisions.
Of course this all speaks to my bias of what a good role-playing game is and what it is not. Dungeons and Dragons was my introduction to role-playing and is my current game of choice. I do not favor the minimalism or free-form/freewheeling qualities to the degree favored by the OD&D crowd, while the detail and thoroughness of AD&D as a rules set isn't quite to my favor either. B/X and BECMI are more to my exact tastes and my ideal balance between freedom (fast-resolving, non thematically-restrictive rules) and structure (rules robust enough to provide a strict framework in which the actions can be quickly resolved). The difference is indeed one of taste, not a fundamental assertion of which is a better, or more authentic, role-playing game.
As long as the action takes place in the mind (and each player takes on the role of an individual character), it really doesn't matter what the theme of the game is. Vampire (excusing any metaplot), which I'd never touch for more personal reasons having nothing to do with gaming or its focus, has a tradition of literature and has even less props used during gameplay than D&D often does. The full breadth of the options of the Tri-Tac combat system are just ridiculous, but as much as they try to describe total realism, the games using Tri-Tac's system are certainly role-playing games in the full sense of the term. Then there are so-called indie games as Sorcerer, Dogs in the Vineyard, and the like (but certainly not everything under the indie or story games umbrella!) which I think are no different than other role-playing games (their creators' intentions notwithstanding), at least no more different than, say, OD&D versus the Marvel Superheroes game.
People talk about how society is moving on and people don't have time anymore and TV and internet and movies are what it's all about and books are just old-fashioned and... ahhh, bullshit. Most people just don't read for fun and they never have. But there are always a few that do, and of those, some read fantastic fiction, and it is these people that should be found, recruited/marketed to (whichever way you want to put it) and brought into gaming. Trying to lure people in using the more popular (and explicit) examples of video games and movies seems to me to be a non-starter, and a recipe to always moving towards more rigidly defined abilities (feats!) or more concretely defined environments (assumed and required miniature usage or virtual applications to replace a gaming surface), and overall less imaginative gaming with less inherent possibilities. I will also go so far as to say that using production values to attract people to the game, rather than to illustrate facets of the game, will also create problems for those new players in being acclimated to the role-playing hobby as a theater for the mind.
Role-playing as a hobby is what it is, and all the new concepts and presentations in the world cannot change the fundamental aspect of having the action unfold strictly in the imaginations of the participants. We're constantly told how rough it is for the RPG market. We need to realize that while many may play in a casual manner, the number of people who care to buy and organize and run these games will always be limited. Our hobby, and our industry, can indeed be large, but it will never (again) be mass-market. And I believe that any effort to change the hobby to enable mass market participation should be avoided. Welcome those that are interested, but do not bend for those that are not.
If what the hobby is becomes obsolete to the point where it can no longer survive, then I wish it a dignified death.
But for all the changes in culture and society, I do believe that telling stories, and reading stories, will endure, whether on paper or on screens, and therefore traditional role-playing games, with codified parameters to resolve actions (rules!) and an abstract presentation that happens solely in the imagination, will endure as well.