Is that an incandescent bulb or a led bulb with a old incandesce bulb form factor? I don't expect a Tesla coil to generate enough current to heat the filament in the incandescence bulb, but they are enough to turn on discharge lamps and leds.
A Tesla coil would turn an incandescent into a plasma globe, a fluorescent will light as normal, and an LED wouldn't do anything. The video is fake.