I figured he meant any omnidirectional gain over a vertical 1/2 wave antenna or
some other reference.

When the "gain" of something is discussed it must always imply a ratio of the
signal strength with respect to some reference.

Common references are a so-called dipole and an isotropic antenna.

For both references you can have omnidirectional gain. My Cushcraft 2-m Ringo
Ranger is omnidirection and has gain.

73 de Jack, K9CUN