When I watched the video, in the selections the RH seemed to have some kind of melody or melodic passage, and I'm assuming the LH was more of an accompaniment. I'd do HS or HT depending on the nature of the music.
In one spot he identifies a chord as missing the 3rd, then states that with the LH it would be a different chord, but he's ignoring that part. I didn't quite like that. For one thing, music often does have common chord progressions and these help make the music predictable for memorization.
I don't know which chord it was so I'm inventing one where in the RH chord the 3rd is left out. In the imaginary chord we're in F major, and the chord including the bass is C7b9 going to F (C E G Bb Db). Our RH notes are E G Bb Db which is a fully dimininshed chord (Edim7) But the 3rd is left out so we have E Bb Db. -- with the LH we'd get C E Bb Db. Is it easier to memorized Edim7 to F ..... or C7b9 to F? I'd say the latter because of V7-I. In fact, the C7b9 would help me remember the E dim7 (where we're assuming the G, btw.)
I'm ambivalent, because I have run into this, where the LH gave the actual chords, but I saw a clear pattern via the incomplete chords for RH alone which actually helped me. I think I preferred to perceive both.