For me its looks like this are against the second law of thermodynamics. They may have a black ritual to bound a Maxwell demon to the graphene or I have not understand this correctly.
I could be reading it wrong, but it seems no different than solar panels really. You're taking something already there in the environment to recharge the battery. The question then would be how efficient is it to do so and is it economically feasible to do so.
Since the thermal energy they're using penetrates, you're not as worried about open surface area. And if power goes up with heat, then this could also be used as a sort of thermocouple to get energy from a thermal reaction.