How can a moving frame transmit energy (a fighter plane shoots a bullet)?

This question shows that a bullet shot from a flying plane receives a large amount of energy from the plane, even much more than the energy from the propellant of the bullet.

But I wonder how can the plane transfer additional energy to the bullet? For example, the propellant gas expands and creates the pressure that pushes the bullet forward, this energy is limited by the propellant itself. While the plane only recoils backward, how can the plane transfer force, or energy to the bullet, in what method since it even does not touching the bullet? If the barrel is a part of the plane, the plane even pulls the bullet backward by friction.