Output Power Level of an Amplifier depends on few factors more not only matching.
-Operating Point and Biasing Current
-Available Power from the Amplifier by Load Pull Measurements ( Optimum Load for max. Output Power )
-Input Matching that ensures the available power from the source is delivered to Amplifier
20dBm is not a high Power Level. Even medium power transistors ( FET or BJT ) may provide this level.
As I understand from your curve, the amplifier is wrong biased because the Transfer function is not regular. Check you biasing conditions