Regret to write, the above does not properly describe the key principle of the hybrid .I seem to recall the benefit of a Hybrid over an ICE was on journeys where more stop-start driving was involved (typically town) and/or hilly routes driven. The energy wasted when braking can be used to charge the battery instead. That was explored and talked about maybe more than ten years ago so 2013 makes sense. Obviously a pure EV would be better as the engine is dispensed with and EVs have been getting better since Hybrids were a thing.
The overarching principle of the hybrid is firstly an IC engine designed and engineered specifically for high fuel-efficiency and usually with a characteristic of weak torque and bhp, weakness of engine torque and bhp negatively affect vehicle operation, reduced acceleration and ability to ascend gradients.
An engineered solution to improve vehicle operation, we add a battery and electric motor to the powertrain, the powertrain which combines the stored power in a battery and the strong torque of an electric motor to supplement the IC engine. The end result is a car of a characteristic of both fuel-efficiency and positive vehicle operation.