He is extremely misleading, if not technically wrong. The Poynting vector has nothing to do with why some small amount of current is temporarily induced into the light bulb. The actual electrical energy flows along the wires (inside and out). In an unrelated phenomenon, you transmit some tiny amount of electrical power directly through the air/vacuum between the battery and the bulb. In a different configuration, or if you inserted certain kinds of reflective materials, you could block (most of) this energy from ever reaching the bulb, without any change whatsoever in the current flowing along the wires. Also, if you submerged the whole circuit (or just the space around the battery and bulb) in a dielectric material with a low speed of light (say, in a piece of rock), you would get a vastly slower and weaker current, with no effect on the current flowing through the wires.

Even the part where he explains the problem with the chain metaphor is wrong. If you actually had a mechanical chain and an engine moving it back and forth, you could extract energy from the movement of the chain either by exploiting friction (to heat up something, just like a resistor does) or by using gears that resist movement in the opposite direction (e.g. slipping the chain) to achieve movement in a single direction. There's nothing all that mysterious about how we extract energy from electricity, at least in practice.

In fact, you could even get an equivalent of the small induced curent: if you recreate his extremely long circuit with a motor instead of the battery and an extremely sensitive motion detector instead of the light bulb 1m away, you would detect some motion [1m/speed of sound in material connecting them] seconds after the motor is started, assuming you are not floating in a perfect vacuum; and then vastly higher motion after 300,000km/speed of sound in chain seconds later.

Nothing more mysterious going on with the EM field.