GNS theory is, or was, a popular theoretical tool for the examination of tabletop RPG game design, though it was mostly fixed upon the player, rather than the game itself. Ron Edwards, and the forum that the theory came from, have a bad reputation in some circles, but regardless of these issues I have found the theory structure useful in the past while working on games and judging the design in terms of something to aim for.
That isn’t to say that GNS doesn’t also have some issues and I’ve been rooting around for some time to improve it to aid with my own game design structure and I think I have hit on the missing element for a structure to examine and design games of most types. The idea of something being a ‘Toy’.
There would, then, be four elements to any game.
Game
The Game factor is the element of skill to the activity. This can take many forms from honing reflexive skills to learning how to build characters with maximum damage output. The Game factor is the amount to which you can ‘git gud’ and improve your personal skill and interaction with the game. Game elements tend to conflict with Toy and Narrative elements.
Examples of high ‘game’, games would include Dark Souls, 3.5 Edition D&D (character builds), or Chess.
Narrative
Narrative is the extent to which story constitutes and controls the activity. Narrative factors tend to conflict with Toy and Game elements. Narrative elements can include story heaviness (often limiting free exploration) and tends to create a more passive, less player oriented experience.
Examples of high ‘narrative’ games would include Choose Your Own Adventures, visual novels or Once Upon a Time.
Simulation
Simulation is the extent to which an activity tries to faithfully replicate something. This does not necessarily mean realism, activities can attempt to replicate the tropes and conventions of unrealistic genres (superheroic comics or action films for example). Simulation tends to conflict with Narrative and can conflict with Game elements.
Examples of high ‘simulation’ games would include Basic Roleplaying, Microsoft Flight Simulator and SSI Wargames.
Toy
A Toy factor determines how much the activity is a ‘plaything’ and how much it is self directed. This is another way of expressing the degree of ‘sandbox’ and latitude a game might have. Toy elements tend to conflict with Narrative and Game elements as a sandbox must allow for latitude and escape from the directed narrative and the constriction of needing to ‘git gud’ gets in the way of freedom.
Examples of high ‘toy’ games would include Lego, Minecraft and Hexcrawl tabletop settings.
You could then plot a game’s position by measuring the tension between these various factors to measure it against other games.
Rotating this 45 degrees and using it as a ‘political compass’ could let you plot and compare games.
There may be a significant problem with this form of breakdown:
You have Narrative conflating two very different things; things so different that they really don't belong in the same bucket.
On the one hand you have story, and by story you seem to mean a predefined, predecided stream of events which the process of play can interact with but not change in any significant manner.
On the other hand, you seem to be defining narrative as mechanics which primarily concern themselves with traditional tropes or "elements of stories" without necessarily requiring an extant story to engage.
Choose Your Own Adventures and Once Upon A Time are not games which engage with the idea of story in remotely the same way. They don't engage with the idea of narration or narrative power in remotely the same way. If anything, Once Upon A Time is the antithesis of what you would refer to as a high narrative game because each player is engaging with the story that they would like to have and taking into account the elements of the story that other players are bringing into play, but there is no pre-existing story that is guiding narration. Exactly the opposite.
By your description, Once Upon A Time should be a low narrative game.
As a result, I find the idea that you have two oppositional axes to be less than satisfying. You're engaging in the Manichaean Mistake, assuming that traits which aren't parallel are opposed.
If you really like this architecture, you would be far better served in presentation and contemplation by making each trait a scaler rooted at zero. A specific instance of a game then has some portion of all four of your indicators and rather than two oppositional axes, you would have four columns in a bar graph or radial distances of a polygon.
This just seems like opposition for the sake of binary thinking.
Let's try an experiment to see if it's possible:
What would a game which is both high in Game and Toy look like? By your system, that should be impossible.
If we add an element of competition to Minecraft, suddenly we have something that breaks your system – and there are PVP mods for Minecraft that form competition in dozens of ways. Likewise there are PVP modes for Factorio, a game about making the most efficient factory and keeping it defended from aliens. Likewise FortressCraft Evolved. There's an extremely high Game factor but also quite a lot of Toy.
Essentially, I can't get behind this from multiple directions. It's just too internally inconsistent.
Quite possible, but it refers to the simple political compass; which by the same definition is never accurate (or, binary thinking need not be wrong if you accept that it grossly simplifies).
I've seen Factorio, but not PvP. On what is PvP based- real time and you compete who will have more resources and / or destroy the opponent? The toy aspect of Factorio is then lessened as it now has a goal and measurement, whereas before we could conversely say it had only a direction. With goal and measurement it becomes a game- it is a system of rules the players compete to navigate in the most efficient manner.
The question is what is the focus of the game; if you had to grossly simplify it to find the only the single most important thread (even if that thread were a non-thread between threads as in opposed mechanics: you must earn and spend $ becomes you must manage $).
Weird combinations do happen, but what is the whole? In our context, the primary point of such distinctions would be of course to create interesting categorizations that stimulate new ideas.
You mean this?
I really like the addition of "Toy" to this theory. I think I have some thoughts on the entire post, but I want to take some time to let it all sink in first.
Still, a solid post and one that I plan on mining for inspiration in my own design work.