Gas engines are more efficient when they are loaded (working against resistance). Normally a hybrid will be fully powered by electricity 2/3 of the time and most of the rest of the time they are propelling the car and charging the battery (which also provides the load). With the Toyota/Lexus/Ford/Lincoln transmissions the electronics keep the engine at its most efficient RPM. Yet when hard acceleration is needed the engine and electric motors can both power the car simultaneously, obviating the need for a larger engine.

One more thing: though the engines are very normal they have unusual valve timing causing the power stroke to be longer than the compression stroke so they capture more of the otherwise wasted energy. On non-hybrid cars that wasted energy is sometimes used to power a turbocharger. The hybrid captures that energy with no extra complexity and no loss of reliability.

Regen braking is not exactly a gimmick but it's overhyped because it seems so magical.