[flatbutt]

He throws so much theory in there that it would be difficult to explain it at all without a foundation in music theory.

His concluding remarks regarding chromaticism vs diatonicism don't go far enough in lay terms so I'll give it a go.

First, consider the notation scale. A note on every line and space. Starting with C and moving up the scale D,E,F,G,A,B,C.
Each of those notes has been assigned a "scale degree" and a name:
C is the 1st scale degree: the tonic
D is the 2nd degree: the supertonic
E is the 3rd degree: the mediant
F is the 4th degree: the subdominant
G is the 5th degree: the dominant
A is the 6th degree: the submediant
B is the 7th degree: the leading note (or leading tone)

After scale degree 7 we return to the Tonic only 1 octave higher.( It would be scale degree 8 but Bach didn't go there.) Note that these designations hold for any scale starting on any natural note.

Each of those notes can be raised (sharped #) or lowered (flatted b) which gives us the chromatic scale when the notes are played in order C C# D D# E F (this relationhip E F is special, more later if you wish) F# G G# A A# B C (BC is similar to EF).

The Diatonic scale is one in which the notes of the scales are defined by key signature. In the key of C major all the notes are natural, no sharp or flat. If a note is sharped or flatted while in the key of C major it is referred to as chromatic or accidental or non-diatonic.

The major scale names are C major, G, D, A, E, B, F#.
In the key of G major there is one sharp G A B C D E F#...G

Each key proceeding from there (which is a 5th above the previous key ie the dominant) adds an additional sharp which is an interval of 5 or a fifth above the previous sharped note.

So, from C major we went to G major C D E F G = up 5 C to G. From G we go to D
major with a C#.

The addition of the sharps is in the order F#,C#,G#D#.A#.E#.B#

Here is where it can get confusing. The scale degree of 7 is known as the leading tone in the major scale (the minor scale is a wee bit different) because it LEADS us back to the Tonic. The leading tone is a half step below the Tonic and so must usually be sharped to meet that rule.

Each note in a scale played according the key signature is referred to as a diatonic scale as opposed to a chromatic scale.

As far as claiming that the video is music history well that is obviously a bit of Lenny being Lenny.

Bach did indeed organize all of the previous mish mash of music writing into a coherent system known as Western Tonal Music. That is a long story for sure.
Hope that helps. Questions? Answers are free.