The rotary (rotating) engine also had the benefit of the entire mass of the cylinders, pistons and crankcase acting like a giant flywheel.
This was a great in keeping it spinning after the guy who grabbed the propeller gave it a 1/4 turn to start it.
As for the gyroscopic effect, that could be good or bad depending on what the pilot wanted to do.
If someone was on his tail trying to shoot him down he could rapidly turn and dive in one direction but turning in the other direction was more than a little difficult.
That could allow the pilot in a rotory powered plane to out turn the pilot using a non-rotating engine if the turn was in the correct direction.