Did you mean Adventure Game?

[Cluedrew]

I am a bit skeptical, purely based on that I care mostly about the RPG and AG, which fits rather strange with that diagram. Or maybe it just explains what I think should be focus for character and player respectively...

I think I am story-telling & wargame myself. I think the answer to this is simple. Most systems have different parts that we can measure separately, not just with this system but many others. As a simple example character creation and pre-game set-up usually looks different than the system mechanics for the main play. Other people I know enjoy social aspects to be much more freeform than the rest of the system and so on.

Perhaps Roll-playing (Gambling) could fit between Story and Role-play.
It's kind of like a challenge, but you don't really think things through and plan them.
And it's not really got the depth of focusing on story, but you do care about events and have to move on.

I mean you could, but the more finely grained you go the less general the description becomes. Right now I am trying to keep this very general.

Ok, third time's the charm?

War Gaming is when you make choices based on the playing pieces, their statistics, what they can do.
Adventure Game is when you make choices based on the player, their problem solving skills and ability to interpret the world / puzzles / etc.
Role-playing is when you make decisions based on the character, their personality, how they react, what they would do.
Story Telling Game is when you make decisions based on what would make for a good story?

It is a pretty good one line of each (I haven't found time to respond). I would add to war games that this also includes creating the playing pieces. So the character creation mini-game is definitely a wargame thing in this model. As for story-telling... yes that sounds about right. I usually prefer the interesting situations phrasing but maybe "making decisions based on how they will shape the story" might be a better way to do it. First it takes the "good" out of it. Not that we want bad stories but good is very subjective as you suggested later in your post.

Can you elaborate what you mean with those deign principles? How does "starting from challenges" differ from "starting from story" and what do you mean by it?

I would probably have to get Cosi back to explain that. It came from a brief exchange we had in Fixing D&D: YOUR WAY starting at post 82. This conversation has kind of gone in a different direction, that was the spark but it fit in with a bunch of other ideas.