Chimneys do not require perfect insulators otherwise no chimneys would work. The biggest thing they do is prevent air mixing which in turn prevents a lot of energy exchange. This could work.
I can scarcely believe that this is an actual level of argument that's occuring on HN.
However, the author is not arguing free energy. That would be like arguing wind turbines are "free energy". It's very clearly a solar powered device, with solar energy providing the heat that drives the air movement.
Regarding the practical issues, what happens at night? Does it collapse under its own weight? How do you get it up in the sky in the first place?
If the air under the chimney needs to be warmer than the air beside it,this could be achieved with mirrors or a broad greenhouse.