was this video shot like a music video, where they had a voice-over, then just shot it like a music video and synced it up to the multiple shots?

Why I Hate Religion, But Love Jesus || Spoken Word - YouTube

I think he is using a wireless lav. There are no mics in any of the side angle shots.
It seems too spontaneous to be looped (unless the actor is REALLY good).

As Richard said it is probably a wireless lav and 2 or 3 takes edit together.

Wireless lav. You can see it in his jacket.

these videos are so annoying. they're impressive at first, until you realize they're just cycling through about three or four shots. I watched the marriage one and it got to the point where I could call the shots... "Medium... punch in... slow track to the left... back to the wide."

Buuuut this isn't the cinematography forum, so nevermind.

Wireless lav. You hear it at 2:06 when he hits his chest.

You can also see the receiver on the camera when it's in the shot.

In spite of the cliches, I like it.