Yes, he could have approached it differently.
It’s really good at explaining the octave, the fifth, it shows the mathematical basis for why just intonation has “wolf notes”, and why we use 12-tone equal temperament.
Once it hits the 12-tone scale, and explains why we generally avoid the tritone, it doesn’t explain very well why we generally use diatonic instead of chromatic scales (well, OK, great music can use chromatic scales, but there’s a reason “Entrance of the Gladiators” sounds like a clown show).
I would had, after explaining how 12-tone gives us an almost perfect fifth and fourth, explained that a major third is 5/4, and a minor third is 6/5, and that the thirds are noticeably but tolerably out of tune in 12-tone equal temperament.
Once we have the fifth and the major third, we then explain the major chord (Base note, 3/2, and roughly 5/4). Next, we explain the perfect fourth. From there, we can show the I IV V chord progression. And once we have I IV V we can then demonstrate the major scale. (The linked article shows us a major scale but doesn’t explain why the major scale is tone-tone-semitone-tone-tone-tone-semitone—it’s that way because if we take all of the notes that exist in a I IV V chord progression, we get the seven notes of a major scale)
After I IV V, I would then look at a basic 4/4 rhythm, quarter notes, eight notes, the kick drum, the snare drum, and the closed hi hat.
I IV V, the major scale, and a simple 4/4 rhythm is enough music theory to write a good number of rock and pop songs.
I IV V and the major scale is roughly equivalent to understanding variables and variable assignment. Adding the structure of a 4/4 rhythm, with kick, snare, and high hat is equivalent to if-then-else and while.
From there, if I were to continue, I would next explain the minor third (6/5) and minor scale, the pentatonic scales (minor pentatonic gives us a large number of rock guitar solos), and probably show the I V vi IV chord progression.
Obviously, this is very basic, but things like ABRSM Grade 5 are the music equivalent of Forth-like and Lisp-like languages: They can be useful, but just as the majority of programs aren’t written in Forth or a Lisp dialect, the majority of music doesn’t use, say, an irregular time signature.