The main constituents of the atmosphere, nitrogen (77 percent) and oxygen (21 percent) play no part in the greenhouse effect. (ase.tufts.edu)
Also, what is to stop the other constituents of the atmosphere from transferring some of their (thermal) energy to CO2 via collisions? (theinconvenientskeptic.com)
Almost all minor constituents of the atmosphere absorb some infra - red radiation - but some absorb more than others.Drawing a clear line between «greenhouse gases» (GHGs) and «non-GHGs» is therefore not easy. (usask.ca)