@mF/7wb5 -
Pretty much. IIRC, they didn't mention it, but you'd also have "stage interpreted for a given state" as in "more brilliant or complex ideas likely pop up when you're in an ebullient or inspired state than when in a depressed state".
Putting on the math glasses, let's speak in the code of mathematics.
Each individual is essentially a point in some kind of space with dimensions yet to be determined. Now lets invent some kind of "measuring stick" or test or way of consistently associating a point with a number or a color or certain turns of phrases or blood pressure or behavior or whatever. A good stick will split points into many but not too many groups. How many is that? Like 3-7ish

Here, Hanzi uses the 4 sticks above. As 7wb5 suggests, there could also be other sticks like temperament, gender,...
Mathematically, each stick is a dimension with a measure. A good measure allows us to classify and classification allows us to abstract a coordinating principle. This group or interval is like that, that group or interval is like this, and so on. Whereas a bad measuring stick does not differentiate (all points measure the same).
Pomo, being mostly a philosophy of critique while not providing much in terms of usefulness on its own (shots fired!) also considers, nay insist on the boundary cases. A measure that is too fine wherein each point has its own category (unique snowflakes) or a measure that contains all points (unity) are not useful measures for the purpose of understanding complexity. (However, they're both good for being compassionate and inclusive. But that's another part of the human brain... I'll get to that.)
The beauty (and good) of abstraction is that it reveals another layer of reality. It is another way of seeing reality. We often have discussions on the forum about the value of "theory vs practice". Theory allows one to see more layers of reality. MHC essentially measures the layers upon layers (recursive applying this idea to itself) that someone will use to interpret reality.
If MHC relates to the frontal cortex
stage ability to abstract (MHC = depth of recursion)---I'm using the triune brain model for simplicity (I'm philosophically an instrumentalist at heart, not a realist. As far as I'm concerned, the triune concept allows me to speak (use code) about it. I don't literally believe that the brain has three completely separate parts

)---then the limbic system relates to
state. What's important here is that state runs on another kind of reasoning than logic. Various set-levels and transmission levels of of hormones and neurotransmitters motivate people (and animals, but not plants) to do things. If these are in stable balance, then the person (point) has
low depth and feels that existence is somewhere around "meh, okay, inspired" (this describes me and the majority of people BTW). If they're volatile=high range, the person has high depth and feels an existence from "hell" to "heaven". We have a second measure and so a second axis in our point-space.
(Note that the abstraction process---which is somewhat different from Hegelian synthesis---requires gathering enough points for a pattern (measure) to be detectable. IOW, deeper and deeper levels of abstraction requires more and more points. The ERE WL table could not have been generated before talking to several hundred different people. As such, ERE WL1-5 are pretty solid. 6-7 are "good enough for government". 8-10 are a working hypothesis.)
Now before we go one adding all our favorite dimensions and measuring sticks, consider this! Many of them are correlated. If so, they can be reduced to each other. We don't need two measuring sticks if they measure the same thing. (This is why the world has gone metric

). For example, BIG5/OCEAN-anxiety measures the same thing as MBTI. It just uses different words. They're both a kind of factor-analysis (make up some reasonable dimensions and measure them) though. IOW, if I know your BIG5, I know your MBTI and vice versa, so I don't need both.
Before going further, I think "code" is tremendously important and useful($). Code is not just words and symbols but also how words and symbols are arranged and especially what kind of abstractions (relative to the previous stage) they're capable of expressing. George Orwell recognized early how important code is. One thing that bugs the hell out of me when it comes to practical postmodernism is the insistence on keeping everything short and conversational in order to be inclusive enough for everyone to "co-create" and feel like they're part of the solution. Fine!

But this also means reducing the MHC to the lowest common denominator of the group. Is that sacrifice worth it for the sake of compassion?
($) This is also why one ought to pursue the renaissance ideal. It was all about expanding the potential code usage as a human being.
Code also explains why "being creative" is way easier when the code covers the water the fish swim in as opposed to when they're trying to swim outside of their code. It's a lot harder for fish to talk about or understand air than it is for cows who breathe air. OTOH, it's harder to cows to appreciate the ability to move up and down as well as back and forward and left and right than it is for fish; because cows don't fly. Note that humans have basically no words for Kegan6 or cross-paradigmatic concepts. We can only extrapolate that this might be there based on some principle. However, once the code is there, the zeitgeist will provide all kinds of "creative" innovations and Stigler's Law will dominate. Before that happens, genius is required.
Code is important because it makes it possible to translate. We can translate to another person but we can also translate back to ourselves. Many humans as well as a handful of parrots are capable of reflecting upon themselves even if some humans and most parrots are not. This reflecting is only(?) possible because of coding and it REQUIRES(?) coding in order to do so. It's hard to talk or think about something when we lack the figurative instruments to do so. That is, if we don't have the words or whatever to reveal the organizing principles, we have to intuit or make them up before we can proceed any further. (This is where and why exclusively practical people never move beyond their current way of seeing and interpreting the world beyond a given stage.)
This of course is but another abstraction: "instruments watching instruments" and so on, turtles all the way down. Then turtles in any conceivable dimensionality you might think of. Code (and the process of communicating in code) is important both for reflecting to other humans but also for self-reflecting to oneself.
Richer code -> richer life-experience. (This is why theory is important!)
If someone has a high state-range but a low MHC they won't be able to learn the code required to express it. It would be like trying count while only having a counting concept of 1,2,many (this is a real thing, there are a few remaining cultures like that!) or trying to describe the color of the wall while only knowing the 16 colors of Windows3.11 (also real, and somewhat more common). Or not being able to talk about feelings because one only knows so many words for the nuances of that. Or describing the feeling of unity in the language of quantum woo, lacking the MHC to understand actual quantum mechanics.
Indeed, they might surmise that state, whether subjective or intersubjective, is THE ONLY AND/OR MOST IMPORTANT VARIABLE. They'll write a paper analyzing the entire world from that one variable from the perspective of the "formal thinking"-MHC state. Hanzi points that out. So we get all these formal-thinking-stage theories that pretty much describe the same aspect of thought. (It took me a couple of years to realize that basically all these models reflect the same aspects of the universe). Each of those can be put in a table showing the overlaps. Wilber has the best maps of those maps.
OTOH, if someone has a high MHC but stable medium state (like me), they won't care much about state-range, because the measure all falls in the same grouping, so therefore it can't be important (for someone with that configuration). IOW, if everything feels more or less the same, then feelings can't be all that important as a differentiator---it's effectively a "rolled up dimension". Compassion, which is mostly an Fe response, falls on deaf ears: "I'm really sorry you're dying of thirst. Come join our community. We don't have any water, but we'll kiss you and hug you and love you and call you George". Green does that a lot! But [compassion and community] is not what everybody in the world needs. Only what some [desperately] need. And vice versa for those who talk about wonderful world of quantum entanglements yet can't tell the difference between the Schroedinger equation and their tax return.
So in conclusion, the keyword is not compassion but width, depth, and consideration.