Yes!! I've been playing this exercise and what I'm seeing is that I can look at the shape and immediately (or almost...work in progress and all that) see where the root is. What I'm working on is recognizing the spacial relationships so I don't have to figure out "What chord is this?" and then "Where is the root that needs to be dropped one note?" The goal for me is to instantly recognize from the shape (and it's placement on the fretboard) what the chord, root and inversion are

Hmmm... Not sure. What I'm trying to aid is the visualization of the chord tone spacial relationships. IOW looking at a specific shape and quickly seeing it as a minor chord in 2nd inversion, or conversely wanting to play a major chord in 1st inversion and quickly fingering the appropriate shape, independent of what chord it is – the shape is the same whether it's a F# or C chord.

This exercise quickly shows your errors as you end up with a chord that is the wrong quality (major instead of minor or diminished instead of major or minor instead of diminished etc.) or the right quality but the wrong root. The name of the "game" is to do this exercise quickly (i.e. no time to "think") and form all of the triads correctly no matter how far you take it.

Could you explain this further?
Music Theory eludes me.
I'd like to hear more.
I play by ear.

I seldom ever look at the fretboard.
It either sounds right or it doesn't.
I play with my eyes closed.

I play keyboards, sax, guitar and Chapman Stick
I play them all as if I were blind.
It helps me focus on the music,
not so much about theory.

I looked up inversions to get an idea of what you were talking about.
Chord inversions are just a rearranging of the notes of a chord such that a note aside from the root is in the bass (lowest) position. Chord inversions allow you to play different voicings and add variety and flavor to your playing. You can start utilizing them in your own playing by incorporating them into chord progressions you already know.

Substitute "spatial" for "visual." Even if you aren't looking at the fretboard, there is still a spatial relationship between the notes. Whether you "see" the spatial relationship is irrelevant. You're aware of it.

As you explain, inversions are alternate voicings of a chord. What I'm trying to get to is being able to construct any of the three voicings for any triad without having to think about it. Knowing that if I want to play a triad with a root on a particular note, that I can place the other two notes on the next two lower strings, the next two higher strings, or one on the string above my "root" note, and the other on the string below the root note. Those are the inversion choices I have to voice that triad. So if I'm doing a simple I-IV-V progression (e.g. C, F & G) I can finger all three chords in root position, but it will sound much smoother if I do Ca (root position) Fc (F/C 2nd inversion) and Gb (G/B 1st inversion).

This exercise helps develop that skill.

Note that music theory is useful for analysis of existing works so that we can understand how a particular composition "works." But that knowledge isn't at all necessary to compose or play music. Ears work just fine. Just ask Lennon & McCartney! Where music theory is indispensable though is in allowing one musician to communicate with another via some medium (like verbally in an online forum) other than actually playing or demonstrating what you're trying to communicate.

And contrary to popular belief, music theory is ridiculously easy to learn. Especially if you're already a reasonably accomplished musician. It's just describing what your ears have already learned. It's a very deep subject but you only need to get ankle-deep in it to find it useful. But getting deeper is really easy too as every new thing builds on the foundation you've already built. Before you know it you're neck-deep and everything makes sense.

And no-one thinks about theory when they're playing.

Steve, thank you for the explanation.
It has answered a few of my questions.

As a side note, does anyone know
what tools Greg used to create the animations
for his tutorial videos. Here's an example:
http://www.greghoward.com/instruction/

The last ten pages of "Stickology...." addresses all basic knowledge concerning chord, scale construction, key signatures etc. It's fairly easy to understand. As the chapter states " it will make you a better Stick player".
Emmett designed the Stick's fingerboard layout to work logically through traditional sonic concepts. Chord progressions, triads, polychords, modulation, transposition, 4ths, 5ths......all comes together with an understanding of structure compared to trial and error. Even the dot/line marker placement compared to guitar or bass inlays is revolutionary and works wonderfully within music tradition.
BTW......to be "avante-garde" just play the notes that are outside these traditions. Simple.

Steve A