Steve4102,
I owe you an apology. For some reason, when I clicked your link I wound up viewing
this video instead of the one you intended. No clue why it happened, but when Jeephammer's description didn't match what I saw, I clicked it again and double-checked the URL and this time got the right one.
Jeephammer,
You're close. The charge, Q, on the capacitor will be measured in Coulombs (the number of extra electrons and missing electrons (holes) on the opposing capacitor plates. This is just the voltage on the capacitor times the capacitance in Farads. The amount of potential energy in that charge varies directly with capacitance but as the square of the voltage, and it is the potential energy that is measured in Joules. J=½FV². If you know the energy of the charge and either the voltage or capacitance, you can then rearrange that equation to give you the charge in coulombs on the plates, though it's not usually something you particularly need to know.
A Watt, however, cannot be used to measure charge. A Watt is a measure of power, the rate at which energy is consumed, delivered, converted, or translated. One Watt is defined as an energy rate of one Joule per second, W=J/s.
So, what the fellow in the video is doing is delivering a certain amount of energy, measured in Joules, at a controlled rate, measured in Watts.
The one thing he is doing that I would change is to use an inductor instead of a resistor to control power. As he says himself, that resistor throws energy away. The inductor is extra cost compared to the resistor, but since you then no longer consume power in the resistor, it lets you use a smaller capacitor voltage or else a smaller capacitance. This would save battery life.