Notice he throws the end of the chain downwards to start the motion. This imparts a force that produces momentum in the chain when, coupled with gravity pushing it down, is enough to overcome the force of gravity holding a small amount of chain lying atop the pile, yanking it up and out of the beaker.
In order for this to work, the beaker will have to be a certain height off the floor to allow enough mass in motion, you have to impart a certain amount of force to get things going, and the chain material needs to be of a certain density and stiffness.
Nothing magical about it, physics professors have been doing this for centuries to explain momentum and force.
