I am puzzled why the site says "Multiply the roof plan area by the
roof pitch factor" in order to get the actual roof area. Why do you
need to know the actual roof area for rainfall calculations? Surely
the plan area should be used.

Because rain does not always fall vertically? Then the actual roof area
matches the ground area from which the roof intercepts the rain (I
think). For example, imagine a very steeply pitched roof and driving
rain.

--
Robin