Under centrifugal force fluids separate into bands based on mass. The same principle as oil and water separating under gravity. Use giant centrifuges to spin compressed air until it separates into bands, then extract the bands corresponding to greenhouse gasses.
I don’t know the energy requirements for this or if there is a better way of doing it. But if you’re looking for blue sky thinking, that’s what I’ve got.
Could you math it out from there and compare it to the Sabbatier reaction or to just plain old trees? I doubt you'll extract CO2 cost effectively that way.
Also taking a quick look at the natural separation of gasses in Earth’s atmosphere, it seems that the uppermost layer consists mostly of hydrogen, helium and CO2, and that’s just under gravity.
I’m not a chemical engineer, but I’ll have a stab at what the energy for the process might be. No promises that I can reach an answer.
However, I get the impression that gas centrifuges are really high-maintenance. Is that right? Or does that only apply to the Uranium enrichment case?
The most relevant published literature I’ve found is this:
http://www.mate.tue.nl/mate/pdfs/5250.pdf
Which is exactly about the separation of CO2, but for natural gas production. The throughput was uneconomical in their case, however it does establish that the principle is sound, it may just need a (possibly very considerable) amount of development.
I haven’t exactly done an exhaustive search though, so there’s probably more out there.