I think that the increased hp is due to the way the roller or rolling road dynomometers work. Unlike a traditional crankshaft dyno or water brake type, these machines rely on accelerating a heavy steel roller and then extrapolating the hp from the torque value determined by the rate at which the engine speeds up the roller. The faster you accelerate the roller, the more torque and thus the more hp. A lighter rotating assembly will spool up quicker thus indicating greater hp.
The traditional type of engine or crankshaft dyno uses a brake or drag producing device to put resistance against the engine. The force needed to overcome that resistance is measured by moving a lever arm against a known weight. In a modern version a water brake provides the resistance and electronic load cells measure the force. These are steady state systems where the engine is held at a given rpm against the load during the measurement. In the Dynojet type dyno runs are just a matter of flooring the throttle and running up to redline, if one held the engine at a given rpm the indicated hp would rise during acceleration and then drop once the roller/drum reached the target speed.
As Jack said earlier, the flywheel does not make power although it does contribute to a tiny amount of parasitic drag, but that is not really what you feel when you swap to a lighter flywheel. BTW the same effect is seen when "wedging" a crank as per Vizards book, just like an alloy flywheel it lightens the mass of the rotating assembly and the engine becomes snappier and you think you have lots more torque and thus hp.