I'm thinking it was agonal breathing - it's way too rhythmic to be anything else, indicating that some deeper hindbrain reflex is activating, trying anything it can to get some oxygen to the brain, as normal breathing [in that state given the obvious anxiety/etc and your body going 'ho fuck something is really wrong] would be a whole lot more ragged and probably much faster. Once the brain's upper lobes go lights out and all higher functions stop, the brainstem will hijack your body to try and sustain itself essentially, and it tries for a very long time. It's also quite unlikely he was conscious at all through most of it, I'd say the last sign of rational thought was when he tried to at least puke in the wastebasket he had next to him, but after that it was just the brainstem flailing around and firing off signals to the nerves. The whole process probably looked far worse than it really was - hopefully, but nobody can really know what someone who's dying is going through other than them.
To bring it back to that Ronnie McNutt video - and I'm gonna spoiler this because it's fucking brutal - for a brief second after he shotgun mouthwashed himself, you can see [because there is now nothing in the way because most of his fucking head is gone] his throat opening and closing, why? Because his hindbrain is still mostly intact, and despite the dude's head being fucking gone, it's still trying to get oxygen to the nonexistent brain.
But generally speaking the lights go out long before the body quits moving and trying to do anything it can to sustain itself.