Any model that tries to condense all RPG priorities under just three banners will do that. But at least one should aim the pillars to be roughly equally broad.
Why?
There is much more pop than classical music listened to. Does that mean that classical, folk, etc should all be bundled into "acoustic" while we need a dozen different categories of "pop"?
Edwards's essays aren't fielding sports teams. They're attempting to analyse a creative activity through an aesthetic lens that is appropriate to the activity.
There are a number of things that he takes
as given about the activity:
* That it involves a shared fiction consisting of setting, characters and colour;
* That there are distinct participant roles, such that much of the action involves one participant presenting situations (or scenes) in which characters who are controlled or directed by other participants find themselves;
* That the activity involves a system (some bundle of techniques, principles etc) for adding to and changing that fiction, with the way that situations are handled being especially important (but not the sole way of adding to or changing the fiction).
He then considers reasons
why someone, or a group of people, might engage in this activity. He sees three reasons:
* To enjoy and experience the fiction for its own sake - he calls this simulationism;
* To show that one can "win" by using one's character in the fiction to overcome challenges that occur within the fiction - he calls this gamism;
* To author fiction with a "point" via the play of the game, just like other storytellers in other mediums do - he calls this narrativism.
The labels are largely inherited from prior discussions (he is very clear why he changes "dramatism" to "narrativism" - because the word "drama" already has another important use, coined by Jonathan Tweet, in talking about action resolution procedures). They may or may not be good ones. But the phenomena they label are clear enough.
Are there many possible ways to enjoy and experience the fiction? Yes. Compare a RQ player to a CoC player, for instance. Edwards coins sub-categories (purist-for system, high concept simulationism) to try and capture that.
Are there many possible ways to think about "winning" by overcoming challenges? Yes. Compare cooperative old-school dungeon-crawling to an arena-combat style game. Edwards coins sub-categories (his two dials of competition which can be tweaked independently: my two examples are low on both dials vs high on both dials).
Are the many possible ways to author fiction with a "point"? Yes. Compare, say, Apocalypse World to The Dying Earth. Edwards coins sub-categories (for instance, high vs low risk) to try and capture that.
None of it is mysterious. Are there other reasons for engaging in RPGing as an activity? I don't think I've seen one presented - given that RPGing is gameplay that involves a shared fiction, the three Edwards identifies - of
experiencing the fiction for its own sake,
winning the game, and
authoring with a "point" - seem fairly comprehensive. Perhaps we could imagine someone who enjoys the mechanics or the maths for its own sake? But then why are they bothering with the shared fiction, rather than playing (say) chess or go or a complicated boardgame or computer game?
The fact that the number of RPGers who play for one rather than the other of these reasons is different isn't itself a reason to distort the analytic taxonomy. As I said, it's not about fielding teams.
EDIT: What is the difference between "GM referencing player-authored backstory" and "story now". Perhaps none - that can be one mode of setting up a story now situation! But most often I think it's not. Most often the "point", if there is one, has already been established, and when it happens in play it is about the experiencing and perhaps evincing of that established point. The "point" is not being established and tested in play. (A similar though non-backstory-related example is playing out one's PC's descent into insanity in CoC.)