The headline is inaccurate. The LED outputs more power than the
electrical power input. The remainder of the energy comes in the form of heat from the surrounding environment. It works by applying slightly less voltage than the LED's bandgap and then relying on electron-phonon coupling to kick an electron to an orbital above the band gap.
That kills off a quanta of energy from whatever phonon mode gave the kick (which cools the LED), and the electron emits a photon when it relaxes back into the valence band. The LED is no longer in thermodynamic equilibrium with the surrounding environment, so heat flows into the LED.
