The whole thing seemed to be engineered for drama, and the “results” are an exceptionally clickbaity oversimplification of what’s going on. It’s like that numberphile thing with 1 + 2 + 3 + …

It’s also more complicated than the lightbulb just “turning on faster than the electric field could travel through the wire”, in fact (depending on the exact circumstances) the current would ramp up very slowly, probably not enough to even meaningfully “light” the lightbulb, and only after the light-speed delay one-way would it ramp up to full-brightness.

Electric field obviously travels in all directions, but the electrons which produce fluctuations in the electric field are constrained to the wire, hence unless your wires are so close together as to basically be connected to each other, air attenuates the electric field wave propagation. This is an actually good-faith reproduction of the experiment and an in-depth explanation: www.youtube.com/watch?v=2Vrhk5OjBP8 .