Here is two diagrams one of a conventional system and the other is... After watching the video... Well you decide.
Before we can explain more complicated circuits to you, you are going to have to take some time to understand the basics. Consider this circuit:
There will be 1.2A flowing in this circuit. The same current flows through both resistors. It does not change since these parts are in series. If the two resistors were wired in parallel, then the current would be split between them. But they are not wired in parallel; they are wired in series.
While the current remains the same, the voltage drop over each in-series component will be different. And the sum of the voltage drops across the in-series components will be equal to the total voltage supplied by the battery.
In this example, since the resistors have exactly the same value, exactly half of the voltage will drop across R1 and the other half of the voltage will drop across R2. The battery is supplying 24V, so the voltage drop across each of the resistors is 12V.
We can now calculate the power used by each resistor. Power equals current times voltage. 12V * 1.2A = 14.4 W
In other words 14.4 Watts are used by R1, and another 14.4 Watts are used by R2. The total power used in the circuit is 28.8 Watts.
Notice that R2 does not reuse the power used by R1. Some power is spent in each, and all of the power in total comes from the battery.
If you now look at your simpler circuit with three batteries and a light bulb, you will see that it really isn't all that different from my example. You have two 12V batteries in series, whereas I made up a single 24V battery in my example.
Instead of two resistors in series like my example, you have a light bulb and a third battery wired in backwards.
A light bulb and a resistor are nearly identical from a circuit analysis perspective. The light bulb turn power into light and heat, the resistor turns all of the power only into heat. But they both use up power, and it isn't really important where that power goes, it is gone.
Granted a battery is not quite as simple as a resistor, but the division of power between the light bulb and the battery works in much the same way as the division of power between the two resistors in my example.
The important thing to remember is that with components linked in series, the voltage drop will be split between them. The split will not always be even, because the ratio of the voltage split is determined by the ratio of the resistances of the components. But it _will_ be split. Therefore the power expended in the circuit will also be split amongst the components.
No magic. No reuse or recycling of power.