This is rather interesting and puzzling. Thibado explains that this device experiences what he terms a "Brownian current" which does not cause any net heating effect. I suppose the analogy is that the smoke particles in Brown's original demonstration have work done on them by the molecules, just as the molecules are continually doing work on one another, i.e. energy exchange is continually taking place within the Boltzmann distribution and the smoke particles become part of that distribution, as they are thermal equilibrium with it.
So presumably this current is also in thermal equilibrium with the graphene and is simply a channelling of random thermal electron motions.
What I can't follow however, is his assertion that they have "re-routed" random thermal current flows into an ordered form, allowing energy to be extracted. That does seem to me to violate the 2nd Law, as it seem to involve entropy reduction. By the same token, it seems to violate it because if you can extract energy from thermal motion in this way you have a heat engine without any rejection of waste heat to a heat sink. Hmm - itchy beard time.
I look forward to someone publishing a more detailed analysis of what is going on here. As things stand, I'm afraid I do not believe in the promise of limitless power from a heat source with no heat sink. There is something wrong.