Hi Nate,
The short answer is Vdd is the peak voltage and we calculate power based on the RMS voltage.
For DC we use P=E^2/R but in the case of a sinusoidal voltage we would use the RMS voltage (DC equivalent) voltage in the power equation and the load impedance that the amplifier 'sees'.
In an RF amplifier the peak voltage is Vdd so the RMS voltage would be Vdd divided by the square root of 2. Squaring this you get Vdd^2/2 so the final equation is Vdd^2/(2*Zo).
I hope that makes sense.
73,
Jim WA2EUJ