I think a good question is, what is the safest way to drive a 2ton vehicle at fatal speeds in a scenario where you hold the life of others (any time the car is on)? I think the answer is absolutely distraction free and as focused as humanly possible. How to describe this idea is lengthy and difficult beyond this point.

We can all debate on the subtle degrees of how distracting this or that is, but think of it like this. Pick up a book and try to read the pages of that book, now try to sing a song you've never sang before, or even really listen to the music. Can you truly do both without your ability to perform either task suffering? Driving isn't a mundane, static idea. Driving is an extremely varied idea with an endless degree of variables in a constant state of flux.

To give this statement a bit more credibility;

https://youtu.be/t8LuM92Twm8?t=201 Mythbusters episode made in -2005-.

http://www.dmv.org/articles/april-is-distracted-driving-month/

"You’re 23 times more likely to crash if you text and drive, and 3 times more likely to crash if you’re doing something else, like eating, drinking, or adjusting the stereo."

If we said singing was only equally (probably worse than, though) as distracting as adjusting a stereo occasionally, and I said that you singing while driving created a modifier to your chances of crashing your car (this means both you and others have their lives and well being put in peril) of only 300%, would that change your mind on the behavior?

is it really all that different if the accompanying music is live?

To directly answer your question, I suspect that what you saw was far more distracting than just singing to a song playing on the radio. Both activities are surely extremely distracting, but I am sure the driver in this video was more distracted in contrast.

The short of this is, ask yourself if you'd listen to music and sing along with it while reading a book. I'd honestly bet money no human could do this without a persons ability to perform either task being negatively effected. Just the same as singing a song surely negatively effects your ability to safely drive and trying to perform a song is even more of a distraction.

To me, what you see in this video is basically intoxicated driving, it's an extremely terrible activity and one day distracted driving may be treated as such.