I don’t have my guitars handy, (so I can’t be 100% sure), but this is basically what's going on.

The feedback you're hearing is one octave apart from the fundamental tone. The fundamental tone (g) is produced at the 5th fret of the D string and the feedback (immediately) is an octave higher. He then slides his finger to the 12th fret (same string without picking) and it produces the D note with feedback an octave higher. That’s basically it really.

I must say however, that this sounds like a Fernandes Sustainer pickup with the Harmonic Sustain Mode selected; this does not sound like natural feedback- especially the way the octave kicks in. A less likely choice would be he used an Ebow and natural feedback, but I doubt it.