I skimmed through it yesterday to get the gist. The title was off-putting --- it is a marketing gimmick that is supposed to sell things with variants like "Your doctor will be angry (at the miracle product we found", and "Everything your teacher told you is wrong" -- there is the risk that a writer has interesting things to say, that will never be read (by me) or watched, due to those titles. But then, if he had called it "An alternate view to theory we take for granted" would
anyone read it - would it sell?
In actual fact he is giving new views to things that tend to be taught. A number of things in there have been the object of discussion with my own teacher, extensively. For example, the "minor key" being defined via the "relative major". This is actually only a device for main key signatures, and music doesn't stay that rigidly formulaic. I did a huge transition a few years ago, where the minor scale became a manner of lowering the 3rd, with the 6th & 7th degree in varying flux, but sort of coming out of the major. We renamed the "ascending melodic minor" (as it is taught) as "simple minor" as it is the same as the major with a minor 3rd, and keeps the function of the V7 and the tritone (stressed by the writer).
The "three minor scales" - esp. the "melodic minor" up one way, down the other, like what? In actual fact, the pattern we tended to learn occurs in one period of music, and less so in another, and the bottom line is that it depends on the harmonies and other things going on. So WHY are students of any instrument induced to play what we call the "melodic minor"? I've discussed this in my lessons, and the author makes this point.
I think he is trying to move from a horizontal (melodic) mindset to a vertical (harmonic) mindset - so if music (in teaching) tends to to be defined via the horizontal scale, he wants to shift the balance to the harmonic side. In actual fact the two sides constantly interact and it's sort of chicken-egg. Since he has switched to jazz, he has also moved toward these sensibilities.
Intervals: For reading notation we need, at some point, to be able to recognize a "third" "fourth" etc., and on the keyboard it is handy to see that notes on two adjacent lines are a third, and dash our fingers into it, adjusting to the left or right per sharps or flats. The aug2 and m3 look and sound the same on the piano, but different in notation. We just have to know that. If we go by ear, not. If I return to violin, awareness of 5ths & 4ths may be very useful, given the tuning of the violin, and the fact of 4 fingers.

...... In intervals we have a dichotomy: the "what it is" as sound, sound quality etc. -- and "how it's written and thus named, for written music.
I don't know about singers tuning themselves to a piano's equal temperament. I compared my singing to the piano when I was in my 50's; thought I was wrong because my Ti, and Mi Fa, were "off" - in fact my ear went to just intonation. I had learned movable Do solfege, and absorbed the flavours ... which also had a feel of harmony to them (I discovered). Violin students - at least some of them - do not go by the piano's tuning. Here he is reflecting his own experiences.
I would NOT want to throw out Tone & Semitone for scales. They have their use. But supplement, yes.
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As a general comment: A while back I coined the image of parents who decide their children will only learn primary colours for their first years. Everything in the house is blue, red, yellow, and maybe black and white. What they are exposed to matches what they are taught. Were they to see green grass, it would cause massive confusion. Were they to ever mix yellow and blue, maybe they'd call that weird colour yellow-blue, not comprehending that "green" exists. (Why is "light red" called pink, btw.?) When I look back at the formal RCM material I first had, it is like that house. You get taught certain kinds of scales, key signatures, mainly diatonic things, time signatures ..... the pieces you get to play, the etudes you work on, everything fits your blue-yellow-red world. You are not allowed to go outside and see green grass. No Debussy. No jazz. Or carefully brought in a little bit later, with explanations about the colour blue-yellow ..... "green" will also be a difficult idea because of your early isolation.
This ramble is the best I can do.