RE (from the OP): I'm confused by having one-half of the dipole tied to the RF transmitter output and to Earth ground. Can anyone explain the electronics behind what is going on?
Just to note that all antenna systems are two-terminal devices — no r-f energy will flow on one "leg" of a dipole without an equal amount of r-f energy flowing on the other leg.
A coaxial cable carries the same amount of r-f energy on the OD of its inner conductor as it carries on the ID of its outer conductor. The r-f current on the outer conductor is confined to its inner diameter due to "skin effect," that isolates the two surfaces of the outer conductor along its length.
At each end of the coax, a path exists between the inner and outer surfaces of the coax outer conductor. So a portion of the r-f energy on the ID of the outer conductor can appear on, and propagate along the outer surface of its outer conductor (or "shield").
This phenomenon occurs whether or not the coax shield has either a direct or an indirect conducting path to a true r-f ground reference such as the earth. IOW, the coax shield does not have the same characteristics for the flow of a-c/r-f current that it has for direct current.
R-F current flowing along a conductor exposed to free space will produce e-m radiation, just as it does when it flows along the two legs of a dipole.