[KarlInOhio]

In the linked animation there is a battery in the circuit which isn't described in the article. That leaves the possibility that the graphene isn't producing the energy at all, but rather acting as the oscillator in an AC generation circuit.

Second, the graphene may not be producing any energy at all, but action as an energy capture device from slight variations in room temperature. Imagine on a large scale hooking up the coiled bimetallic element in a thermometer to a generator. As the room heats up it turns one way and as the room cools it turns the other. You would get a little bit of electricity from that.

[Red Badger]

... but rather acting as the oscillator in an AC generation circuit.

From the article:

Thibado’s team found that at room temperature the thermal motion of graphene does in fact induce an alternating current (AC) in a circuit, an achievement thought to be impossible.