This is false. Solar panels do not violate the laws of thermodynamics. Generally the sun is quite a bit hotter than the environment in which the solar panels operate, which are the correct temperatures to compare in this case.
"harvesting energy only from the fastest of them" actually does violate thermodynamics and, if possible, would constitute the biggest revolution in physics in all of history.
The paper claims to generate energy "without a temperature gradient." If there's a hidden temperature gradient somewhere, then the paper is still incorrect.
Given the extremely small power levels, I expect that if it's not a hidden temperature gradient (eg between local air temperature and local radiant temperature, similar to PV) then they're actually seeing some sort of static electricity or air movement effect.
Yes, it is probably better described as a shitty battery NOT a thermoelectric.
They don't, but depending on one's understanding an perspective they can be described as violating. The point is that just because something can possibly be described as a violation does not mean that there are perhaps other perspectives that may understand them without such violation.