The narrator is being a little vague and misleading in claiming that there are only 12 chords.
I could do him one better though and claim that there are really only 4 chords; major, minor, diminished and augmented.

But that's not telling the whole truth as there are literally hundreds of chords in the entire 12 tone chromatic universe, but there are only 12 root notes to those chords (but only if you're talking sharps OR flats).
He gave it away in the second video in saying that each of the 12 tones on the keyboard "represent" a chord, but doesn't tell you that any one tone can have dozens of options of chords based on it.