My understanding is that the main advantage of the rotary engine was that it did not need a flywheel, because almost all of the mass of the engine itself acted as a flywheel. So it could be a lot lighter than the engines that needed a flywheel--which most did, because early on they didn't have very smooth-running engines. Especially if you controlled your power by killing the ignition to some cylinders.
The term "rotary" is a bit overloaded. But the engine shown in the first post is definitely an aircraft rotary engine. The crank was bolted to the firewall, and the prop was bolted to the engine block.
-soD
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