A quick pitch is illegal and considered an illegal pitch. As Steve said, I didn't see what had happened in the video. To be honest, I have seen pitchers use a very deliberate motion to the plate and then vary it with a quicker motion. I see nothing wrong with that. The idea is to keep the batter off balance.
A quick pitch is usually when a pitcher gets the ball, immediately steps on the rubber, and pitches really before the batter gets set. You see this a lot when a pitcher, while in the set position with a man on 1st, will step off the rubber and immediately step back on and pitch. The runner and the batter will usually relax a bit when they see the pitcher step off and for him to immediately step back on and pitch, is and should be illegal. A quick pitch, with runners on, is a balk. If there is no one on it is called a ball.
Any illegal pitch is a balk with runners on and a ball with no one on.
If the pitcher lost contact with the rubber, I would think a base umpire would call that as it would be almost impossible for the plate man to see that.