It's not a neck mopping throw because if your side kick at your opponent's chest, his arm that you are holding must be straight in order to give you enough distance for your kick, it will be too far for you to move your hand on the back of his neck.
The force is not to pull your opponent's head down but to "pull and twist your opponent's arm sideway and backward". When you use your side kick to straight your opponent's arm, both of your hands are holding your opponent's right arm. If you step in your right leg (1st step) and then stealing step your left leg (2nd step), you will move yourself under your opponent's right arm and a bit behind his right shoulder. If you just pull his right arm toward his hand direction and twist it downward, you will create a "flip" force on him and throw him forward. I have never seen anybody be able to use this move in tournament. As Lucas had pointed out, if you can make your side kick work, the throw may work after that. If you can't make your side kick work, since you have to move 2 steps, that will give your opponent too much time to react. This will make the move a low successful rate. It's a good demo move but not a good combat move.
A realistic "solo" combat throw should be able to be executed within 1/2 second. Any throw that take longer than that, the successful rate will be lower. If you have to borrow your opponent's force, your speed will depend on your opponent's speed, that will be a different story.