An assembly is provided for an aircraft. The aircraft assembly includes a rotating structure, a geartrain, a propulsor rotor and an electric machine. The rotating structure includes a turbine rotor. The geartrain includes a sun gear, a ring gear, a plurality of intermediate gears and a carrier. The sun gear is rotatably driven by the rotating structure. Each of the intermediate gears is between and meshed with the sun gear and the ring gear. Each of the intermediate gears is rotatably mounted to the carrier. The propulsor rotor is rotatably driven by the carrier. The electric machine is coupled to the ring gear.