What are the extra microstrip elements on this RF amplifier board for?
Those small islands are there for tuning the input and output impedances seen by the power amplifier. They're not to be removed! Another example (it's common practice, in fact):

 

You can solder several of them together in order to build a stub of the length you need, placed at the distance you need for impedance and/or noise matching.

There are also sections of different width at the output. You can tune the length of each section by soldering some of those islands together.