What is the term for heat transfer because of the movement of a gas?
Depends on if it is a lateral or vertical transfer.
I am answering as a meteorologist, but the same terms are used in physics.
Advection is the lateral movement of a property of the atmosphere (or gas), be it humidity or temperature.
Convection is the vertical movement of a property of the atmosphere (or gas), be it humidity or temperature.
Convection can also mean the circulation of heat by the movement of a fluid. It is only in meteorology that it is vertical motion. So chances are the answer that is most correct is convection.