The Crimson Binome
Right. Everyone agrees on that, which is why it makes sense for RPG to be the umbrella term. The question is how to sub-divide them, so that you end up with useful categories. Segregating all of the games that contain storytelling elements into their own category is a logical way of doing so, from the perspective of anyone who wants to avoid playing those types of games.But, that's not the spectrum. You don't do storytelling games without role playing. At least, not when we're talking about RPG's. Role assumption is fundamental in all role playing games. If you're not taking on a role, you're not playing an RPG. That shouldn't be controversial.
As a side note, I would disagree that you need a random element in order for it to be a game. Chess, for example, does not have any random elements. (Unless chess was debunked as a game earlier in this thread, and I just missed that by skipping to the end here.) You definitely need to play a role, though, and exist within a causal world.A role playing game needs all three elements - role assumption, some sort of random mechanic for determining outcomes and a narrative that follows causal links. Without any of those three, I'd say you aren't really playing an RPG.
Storygaming is not a term which has yet been defined. As a game element, storytelling is the opposite of roleplaying, because it involves the player just deciding stuff without actually playing a role within the world - you're just telling what happens, because the player has assumed authorial agency within the narrative beyond that which is granted by the character.So, no, roleplaying is not the other side of the spectrum from story gaming. There's a reason you still have a character in story games - the presumption is, you are going to act in accordance to the dictates of that character. Granted, in a story game you ALSO have degrees of authority over the game as a whole, but, you still have a character in front of you.
Inspiration is not purely a player resource, though. It has meaning within the game world, in much the same way that a barbarian's limited number of rages per day has meaning within the game world. It's just kind of nebulous and hard to define.D&D doesn't stop being a role playing game because I use Inspiration (a purely player resource) to affect some change in the game world.
The character doesn't decide to spend Inspiration to gain advantage in this particular situation, but the player should recognize when the character is inspired, and use it to represent that. Given that Inspiration is handed out by the DM in situations where it is appropriate, and the DM can easily veto inappropriate uses of Inspiration, I would say that it's working mostly as intended as an in-game resource.
The same is not necessarily true of Action Points (from various earlier d20 products), or Hero Points (from Pathfinder), or "bennies" (from whatever game would be silly enough to assign such a common name to a significant game mechanic; you might as well call them "steves" or "freds" for as silly as it sounds).
In many cases, these resources are only given when the character suffers by playing into its flaws, as though there is some sort of karmic connection between, for example, wasting money on alcohol and later succeeding on a difficult skill check.