Very good video. I think mains hum heavily contributed to this effect. It would have been rectified by the gate's PN junction, causing a negative charge to build up. He said another power source is required to provide a negative voltage to turn the FET off, which is not strictly true. If he has exchanged the positions of the FET and LED, then it could be made to turn off, by connecting the gate to 0V.
It's not just FET circuits which can behave like that. A BJT circuit can do that to, if it has enough current gain. I experienced it today with a circuit composed of an NPN-Darlington, connected to a PNP BJT, forming a super-Sziklai pair. The current gain was so high (2 to 10 million) things normally regarded as insulators, such as plastic, turned it on.