By restricting amps he prevents electrons from entering the water bath, like a capacitor, you don't have electrons flowing between the plates, just voltage across the gap. There is unavoidable leakage, but it is not part of Stan's process.
When Stan says 'liberated electrons' he means the valence electrons are pulled right out of the water molecules by the voltage, then they would want to join back up with the gas atoms to stabilize, but Stan says "i really don't want to stabilize", and this is where he goes into the electron extraction circuit, by applying a positive voltage across a light bulb connected to the cell, the cell acts as a negative terminal, and the liberated electrons and drawn out of the water bath and used as electricity to run the light and so on.