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.