When you perform a load pull, you connect various complex loads to an amplifier output (either in reality using a load-pull setup, or in a simulation like non-linear periodic steady-state analysis). Then the output power is plotted on the smith chart. Usually people will draw 'circles' connecting the point that have the same output power, or efficiency, or some other performance metric.
The reason this is done and can't just be computed from some static S-parameters is because the non-linearity of an amplifier modulate the impedance it presents. This means that depending on the signal level, the ideal output match is different (which is why load-modulation is a common way to improve efficiency).
In this case, the authors would need to know what output power is produced by different output impedances, so they can use this output-match as a output-power modulation technique.
With the 'slap on a big capacitor', I meant that for an RF amp, you usually start with a good low-impedance supply line - which is equivalent with a short at your frequency. You create such a low impedance by having a local decoupling capacitor on chip. You add an inductor between the supply and the PA transistors to tune out the capacitance of the gate (in a sense it forms of your matching network).