The other problem I had was that I thought it was an arbitrary division of the space of aesthetics. It was useful and interesting, but for example I distinguish between the aesthetics of fantasy, competition, and challenge and typically find that players heavily invested in one are invested in the other two. But if you try to map those aesthetics to GNS theory you don't end up with easy mappings
they don't match because they're different panes of measurement. Low-interaction ones at that.
which to me says that GNS can be obscuring what is actually going on at the table and why players enjoy or don't enjoy the game.
I know guys who love AD&D2, but hated Buck Rogers, despite the same mechanics, but the different setting elements.
There is the mechanical pane - GSN is a good description for pure mechanical considerations. A guy who likes heavily simulationist is more likely to enjoy other heavily simulationist designs, too...
but that's utterly unrelated to how fantastic/magical the setting is, how much the game is in competitive play vs coperative play, and how hard the game is as a player to succeed at, and how hard it is for the characters.
It's possible to do high levels of magic/fantasy/unreality in ANY of the three points... DragonQuest and RuneQuest both tended heavily towards Simulation; D&D more towards gamism (but it's not AT the G point), and Houses of the Blooded to Narrativism - and all three are very much "7 impossible things before breakfast" levels of fantasy. Ars Magica is on the sim/narrativist edge; fate on the gamist/narrativist edge...
Competition is most obvious when baked into Gamist games, but it's doable in all three... but the game I've run with the most in-group competition has been Burning Empires - because it handles it well, as does Burning Wheel; Trek has often had soft competition between players for whose idea gets the green light... and the systems ... FASA was almost to the S end along the line with G... STA is pretty solidly smack along the GN edge. LUG is more in the middle, but a step towards sim... (and is my favorite of the three... but PD1 is my favored ruleset)...
Challenge isn't even a clear enough term... is it difficulty for the characters? Difficulty for the players? Is it simply that the envisaged rolls seem off?
I've seen narrative games that stumped players hardcode... but if they could wrap their brains around them, the success rates followed easily. And games that, while simple on the players, have failure rates for the character that are "piss off the players for 6 weeks to get to room two" - I have done that by accident in Tunnels and Trolls - with a player puzzle involving the techniques of a flush commode to keep an entry trap ready to douse and ignite the kerosene... the sparks from the door frame. No magic needed (save maybe to make the droplet dispersal plates). That puzzle would have taken them the same amount of time in D&D, or in AD&D 2, or in GURPS, because the challenge was not mechanical, but a part of the fiction. That it nearly killed them 12+ times? That's the mechanical part, and wasn't very bad... make the SR4 save on Dex (or another att if justified) or take half the difference between needed and rolled as fire damage.
Doing it in GURPS wouldn't make it much more character-challenge, 1d6 damage on fail...
They don't match because their not exclusive of any of the 3 points in GSN, and a spectrum line/plane/space needs 2, 3 or 4 points that are mutually progressively exclusive.
Mundane vs fantastic is a good linear spectrum, but it isn't opposed to any of G/S/N.
Competitive vs cöoperative is a linear spectrum, but its possible in munane or in fantastic settings.
Challenging for characters (IOW, high failure rates) can be part of highly narrative or highly simulationist, or highly gamist games...
Challenge for players isn't even one thing, either, as it can be difficult rules, difficult situations to negotiate, or poor descriptions by the GM... it's not a coherent spectrum until you add the simplicity point and get a tetrahedron... Good descriptions without difficult to navigate situations and without hard to use rules is simplicity for the player in a nutshell...