The Argentine composer he referenced was Alberto Ginastera. Regarding the thirds and classical guitar, he's talking about playing the chords with tenths instead of thirds. A tenth is the same as a third, one octave higher. When he demonstrates the chords at 7:13, he's doing it as a very fast arpeggio. I suppose that, between the arpeggio and the fact that the third is actually a tenth in many guitar chord voicings, this (for him and/or Ginastera, at least) mimics the sound of a guitar being strummed.
He also discusses the chord voicing moving up (which is called chord planing or parallel harmony), which he says is, "very impressionist, very Debussy, very Ravel."
He then goes on to explain that he is "setting up harmony for later in the piece, where I have the B♭ [major chord] which is the ♭VI." He then corrects himself. "Well, it'd just be VI in D minor." He goes on. "When you have that against the V [the A major chord], it creates that half-step tension that I thought was also very beautiful."
Finally, at 8:08, he discusses the harmony moving from A to G to B♭, calling the G to B♭ a chromatic mediant (already pointed out in the comments). At 8:29, when he says that this goes from major to minor, he plays both chords as major chords, which is confusing, but the minor he's referring to is the G to B♭ relationship.