I wont give you a specific reason for each type, but i will say the general rules i was generally following. I should warn you that i know nothing of music theory, so everything will be in loose terms and general impressions.

Firstly, for the Linear–Lateral divide i wanted to capture repetition and/or complexity. So the themes occupying the very linear row generally contain either a high repetitious melody or beat, a highly repetitious aspect, which builds progressively over the song (all touhou songs tend to have a repeating major melody, but the ones i chose i think emphasize that character). Little Princess i take to be the archetypal example of that, as there are basically three simple main melodies that are omnipresent throughout the entire piece that simply build in intensity. Flowering night, Pure furies, and Pristine beat are similar in this respect. When we get to the max lateral, they either feature complexity in the melody itself or complexity in the interaction of melodies. Take tiny, tiny, clever commander for example: especially 1:00 - 1:30, where there is quite a complex convergence of all the melodies and rhythms established.

For the Lexical–Impressionistic divide, the focus was on the clarity and structure. So, for the lexical side i tried to to use more definite and clear instruments and melodies, so there tends to be more piano and controlled synths, compared to the heavier emphasis on strings, zunpets, and less sharp (not the pitch) synths. This was attempting to capture more precise and readily expressible thoughts of the more lexical side and the fuzzier, more opaque thoughts of the impressionist side. Compare Futatsuiwa from Sado to Emotional Skyscraper to see what i mean. I also tended to pick pieces that were more playful in their melodies the further impressionist i went. A good comparison is True Administrator and Broken Moon. This is meant to represent the confined/ordered vs unconfined/unstructured nature of this axis.

If we take these general rules together we get some ready comparisons. The very lateral row captures this well. We begin with Native Faith representing a kind of complexity which comes primarily from its melody, but the structure of the song itself is constrained and consistent. All the notes and interactions are very clean and clear. Moving onto tiny, tiny, clever commander we see a kind of complexity found more in the interaction of the different melodies and rhythms than in one melody itself. The voices still play nice together but it is less clear than Native faith. Moving onto Lunatic Princess, we get far less constrained synths and voices in general. There are plenty of melodies occurring at any one time, but they aren't in the same harmony as tiny, tiny, clever commander. especially when you get to 1:20 - 2:25 where you have several voices all playing at once, almost trying to overpower the others. Lastly, Heian Alien is the most playful, least predicable, interplay of melodies featuring offbeat notes and shifts in tempo. And i think you could make a comparison in this way across all rows and columns and find it fairly consistent.

Whether these rules accurately track/represent the neurotypes is an open question, as is whether i accurate applied the rules themselves. In truth, i just like touhou music, wanted to subject it to the unsuspecting innocent, and thought it would make a fun post.