I just went through the video. (The term "popular abridgment" is unfamiliar.)
I suppose that if you want to learn which notes to play by copying somebody's hand, and you can't read notes much, it might give you that part (either in the wrong octave, or in the right octave but written wrong). In the "analysis" the chord explanations are incomplete which can lead to wrong understanding, and there is one error. The chord at 3:55 is not a "minor C7" -- It is a C7. Since this is a classical pianist, he is probably more familiar with Roman Numerals (dunno).
In introducing the first chord, he says that "every note can have its own scale". There are many kinds of scales so I went "huh?". If he is trying to say "major scale" it would still be wrong, since the 7th note of G major is F#, and he is pointing out the F (natural).
breaking down and correcting the "info"
The chords for the first part, in order, are:
G7, C(maj7), G7, C7, F(maj7)
In each case, the 3rd of the chord is left out, but we still can "hear" the whole chord in the same way that if I write "mny peopl like ths" you will mentally fill in what is expected.
G7 --- GBDF
C(maj7) - CEGB
C7 - CEGBb
F(maj7) - FACE
So he is using two kinds of "seventh chords" --- X7, and X(maj7). The "X7" is also called the "dominant 7" chord, even though it doesn't always have the dominant function (don't worry about that part).
X7 or "dominant 7" is a major chord topped by a note that is the interval of a minor 7th from the root. Or you can say that it is a whole tone (or 2 piano keys) down from the octave. So GBDF, the F is a whole tone down from the G octave. The major 7th interval is a semitone away, and part of the G major scale.
X(maj7) is a major chord topped by a note that is a major 7th from the root. That is also the 7th that is in the major scale if you played up from the root note, and it's a semitone down from the octave.
He skirts around the problem by just saying something like "this chord".
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I would NOT follow the "cookie cutter shape" suggested at 1:29. Many self-taught students are those with poor non-observant teachers fall into the habit of a rigid pre-shaping of the hand. Some of us fell into this and had to relearn (Dr. Mortensen has some excellent videos on this). If you want to know how to move your hands, watch the beginning of the video where he plays through the piece and look for the relaxed fluid motion.