By extended harmony, I mean a major, minor, diminished, or augmented chord that has additional thirds stacked up on top of it, with the numbers representing the intervals above the root (for example, the BbM7(9) from the above track is Bb D F A C). And unextended harmony is just the basic three-pitch chord with no additions.
The notation conventions for these extensions vary a bit depending on whom you talk to, but generally:
if min, mi, or m is specified, the unextended chord is minor
a plus sign, aug, or #5 means the unextended chord is augmented
a minus sign, dim, or mb5 means the unextended chord is diminished
if there is no min/aug/dim etc. then the unextended chord is major
if maj or M is specified, the 7 is a major seventh interval over the root, otherwise it's a minor seventh
9 is assumed to be a major ninth; a minor ninth is written as b9, and an augmented ninth is #9
11 is assumed to be a perfect eleventh; an augmented eleventh is written as #11
13 is assumed to be a major thirteenth; a minor thirteenth is written as b13
listing an extension implies that all the lower extensions are also present; if not, add is included before the extension (e.g. Cadd#11 is C E G F#)
if the bass note is not the root of the chord, the bass note is written after a slash (e.g. C7/G is C E G Bb with G in the bass)
So CM13 would be C E G B D F A; Cmi13 would be C Eb G Bb D F A; C13(#11) would be C E G Bb D F# A; Cmi7addb13/Eb would be C Eb G Bb Ab with Eb in the bass; and so forth.
In classical music, these chord extensions were considered dissonant, and they were generally approached and left by step because doing so makes the dissonance "make sense" in that it is both led into by and resolved into notes that are not so dissonant against the underlying unextended harmony. And the song in the OP specifically doesn't do this, which draws attention to the dissonance. I think the F-C-F jump in particular is important to the overall sound of the example both because it's emphasized through repetition and because the way in which it's dissonant -- that is, the extension that it forms over the chord -- and the specific notes in the gesture that form the dissonance are different in the repetition from in the original. So when you hear it a second time, it's still dissonant, but it's dissonant in a different way. It's the old trick of recontextualizing a melodic figure, which is an effective compositional approach in pretty much every kind of music.