If it's simplified to the point of being unusable, it's wrong.

But that's exactly the point, it is useful, but let's first get to the evidence.
Claim:

It is obviously possible to be both strongly Game and strongly Toy. There is no natural definitional opposition there.

but then you say:

The usual PVP mode is a race to see who can get the first rocket fired into orbit.

A race's no toy, it's a full blown game.

all of the teams competing are on the same physical map in different locations and blowing up your enemy's factory facility

Now that sounds like a regular RTS and that's a game. That's why I said the toy aspect is lessened.

then you're going to have to seriously argue that Minecraft turns entirely into a game only when I start building a nerd poll to see how high I can go – and instantly reverts if I jump off, but only so long as I am not curious as to how far I can fall before I die on impact.

Almost. Not any goal is enough for it to be a game. E.g. if there's a high score for the highest building, it leans into the game territory. Just by the player having decided a goal for themself don't make it a game. The goal must be put up by the game.

In fact, there is not much to be done in Minecraft based on the demands of the game. That's what makes it a toy. And that toy (Minecraft) may contain games: such as creepers at night, or the rules that govern upgrading materials etc. Those are game elements, inside of the overarching no-specific-goal-is-forced, i.e. inside of a toy.

That was just for the point of clearing up the distinction. I don't necessarily prefer to call Minecraft a toy, but that's a topic for some other time.

You are making the assertion that toys cannot have both goals and measurements

Like I've said: not any goal, and not any measurement. The goal must be integral to the play for it to be a game, and the measurement must serve the players' progress towards that goal.

If an infant plays with a ruler it don't mean we have measurement. Just kicking a ball (playing with a toy) don't automatically give you football (you'd need the goal of getting the ball to through goal frame).

It is obviously possible to be both strongly Game and strongly Toy. There is no natural definitional opposition there.

First of all, neither is it obvious, and neither is it even sure that there is no natural opposition.
Lemme restate my claim:

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?

Secondly, lemme address the overall logical fallacy of false dichotomy claim here.

This is actually part of why GNS was a terrible system in general, because it tried to describe as a fixed entity systems in a way that would act as a predictive measure for behavioral interactions, when the entirety of the systems that they wanted to describe were the behavioral interactions themselves. They got lost in the map trying to find a way to the next city and just couldn't deal with the idea that the map was not the terrain.

If it's simplified to the point of being unusable, it's wrong.

Nah man, that's exactly the point. GNS theory, and this post too, although less, mostly because it's shorter, do have use. The use is:

In our context, the primary point of such distinctions would be of course to create interesting categorizations that stimulate new ideas.

You say:

You've effectively defined yourself out of making any kind of reasonable assessment of a thing.

And I say: Yep. No reasonable assessments here. Not academic categorization. Instead, stimulation. (The "wow I never thought of it in that way")

And finally, I invite you to check out my comment on this post in which I state what I found most important.

I really enjoyed this discussion so far.
Cheers :)