Why A gamma match taps the driven element off-center with a gamma rod running parallel to the element. That rod and its connection behave like a shorted transmission line stub plus added conductor length, so the feed point looks resistive plus a substantial inductive reactance. A capacitor placed in series with the rod contributes negative (capacitive) reactance that cancels the inductive part, leaving a nearly pure resistance close to 50 ohms for the coax. Adjusting the capacitor and the rod tap point together tunes both reactance and resistance to a match.
Watch out Transforming the impedance upward is the job of the tap position along the driven element, not the capacitor; and while the capacitor does happen to block DC, that is incidental, since a gamma match is used on grounded-element beams where DC isolation is not the design goal.
Gamma rod adds +jX, so the series cap supplies -jX. Capacitor cancels coil.