If we take the press release at face value, in this device there is no difference of temperature. So if the Second Law of Thermodynamics is correct it is not possible to extract some useful energy to do something interesting, like turning on the lamp in the animation.
The above quote is from the abstract, and just before it, we see the much more reasonable "numerical simulations show that the system reaches thermal equilibrium and the average rates of heat and work provided by stochastic thermodynamics tend quickly to zero."
It make sense, but the problem is more subtle. It's better compare the clock with a brick.
In the example of the clock there is a temperature difference that can be used to extract "useful" energy. You can use it to move the clock, or make a sound or light or something.
(I'm saying "useful" as in the a quote of the main author of the paper "What we did was reroute the current in the circuit and transform it into something useful.” .)
If you put a brick in a oven and keep it at the same temperature for some time, until the temperature, humidity and other properties have stabilized, you reach thermal equilibrium. It doesn't mean that the heat energy in the brick is perfectly constant, it exchanges heat with the oven. The heat energy has small random variations.
But unlike in the clock scenario, you can't use this additional accumulated energy for something "useful". To check if it is in a high or a low, you need a variant od the Maxwell's Demon. You can measure the energy exchange and analyze the theoretical and experimental properties anyway.
(Also, if you put the clock in the oven at a constant temperature for a long enough time, it will stop working.)
Stealing the name from a sibling thread, to make the grapheme device produce "useful" energy, you probably need a Maxwell's Diode.
What is 'the problem' that you are apparently trying to address here? Everyone in the discussion is well aware that the 2nd. law of thermodynamics prevents the continuous extraction of work from ambient heat without there being a temperature difference. Are you saying that the paper is claiming that this has been done? If not that, are you claiming that the device, as described in the paper, is incapable of generating power from fluctuations in the ambient temperature? Have you identified some other problem in the paper? Alternatively - I don't think you are saying this, but I will put it in for completeness - could it be that you are saying that the paper shows that this team really has invented a Maxwell's diode, capable of continuously extracting work from the ambient heat of a closed system in thermal equilibrium?
If you are still only taking issue with the press release, you are just nerdsplaining to a bunch of people who already get it, thank you very much.
Another way of thinking about it is that random noise although uniform at large scale, is intrinsically noisy when you zoom in.
Basically, there are always local micro gradients even though the macro integration of those gradients gives 0. It may as well happen that graphene being few atoms thick and thus dipping into the local scale properties may bridge and aggregate without [total] mutual cancellation those properties into the macro scale (graphehe sheet vibrations may happen be [one of] such a filter, kind of piezoelectric effect). There is no violation of the 2nd law as extracted work/energy wouldn't be larger than the entropy increase resulting from the smoothing of the micro gradients (bringing the Universe's heat death closer).
Or even imagine a pond with no visible movement of water and place over it a myriad of very very small water mill wheels - they will be rotating chaotically back and forward due to small perturbances in the water (and the smaller a giving wheel the larger share of local gradient it will be extracting as the smaller share of it will be mutually cancelling with the neighboring gradients under the wheel). That chaotic rotation of that myriad of wheels can be aggregated into usable work/energy.
