I'm not seeing any errors in the 3D diagram other than maybe the fact that the magnitudes are not reflected? It's the interpretation of the Poynting vector that is incorrect.whatever error you are seeing
The Poynting vector between the wires are non-consequential in DC steady state. Outside of DC, they're called inductance and capacitance. At the instant the switch is flip there is some RF & capacitance effects that'll induce "something" in the bulb. This is why he is correct on a technicality. But most of the power isn't delivered until the circuit reaches DC steady state which take 1s.
The example is to show that DC steady state is unaffected by changes to Poynting vectors between the wire. In other words... majority of power deliver in such a circuit is still flowing along the wires.Unfortunately, I think this example is getting away from any point I can absorb.