I always thought it was Anime Music Video myself, simply because "animated" could be anything - most of the Gorillaz's music videos are animated, but would probably not be considered AMVs. At least that's the way I understand it.
And I loved the Vegeta's Life one when I watched it, so I'll have to check out the others too. You did a great job with it, the syncing and the pace were perfect. Kind of makes me curious about other ways I could use you on the project... ;)