How does a Capacitor generate a potential difference even after disassembling the Capacitor?

In a dielectric induced charges only exist in the presence of an electric field. So, when you disassemble the capacitor all induced charge was supposed to disappear. And it does if you apply low voltage to the capacitor. However, in the demonstration of the video you provide a high voltage is applied to the capacitor and corona discharge pumps free charge into the dielectric (not explained in your video). This free charge is not easily removed from the glass and remains there for the whole experiment. When you assemble the capacitor again, it is that free charge that passes from the glass to the conductors that gives rise to the spark. The experiment is made possible by combining materials with different dielectric strengths and high voltage to induce corona discharge from the metal to the dielectric (through air) but not inside the dielectric.

The detailed explanation of this is given in the video below starting at 32:30:

https://www.youtube.com/watch?v=By2ogrSwgVo&list=PLyQSN7X0ro2314mKyUiOILaOC2hk6Pc3j&index=16