Look at the second link at 41:44. We see those sparks, we see his jars, we have an estimate of the ammount of power in in the spark.
How much power do you think it takes to turn?
Also, do you have issues with heat pumps?
I have two empty rooms of equivalent tempature separated by an insulated wall and I use an air-source heat pump with a COP of 1.8 to transfer heat from one room to the next. I spend 100 watts of power to turn the compressor in the pump, and for every 100 watts worth of electricity I spend I relocate the equivalent of 180 watts of heat from one room to the other.
You have no issues with relocating thermal kinettic energy with less power than you get out.
It's the same here.
The electrons in the cathode side came from the anode side.
Look at the second link at 41:44. We see those sparks, we see his jars, we have an estimate of the ammount of power in in the spark.
How much power do you think it takes to turn?