This is one excellent question.
The answer is that fuel in a moving rocket have some kinetic energy. It is moving at great speed relatively to the Earth after all. Amount of this energy depend on how fast rocket is moving and, somewhat surprisingly, rocket engine can extract this energy and convert it into useful work. You might notice that a formula that you shown is achieving 100% efficiency when velocity of rocket is equal to velocity of rocket exhaust (v=ve). This is so because when v=ve the exhaust speed relatively to earth would be zero and all kinetic energy stored in fuel will be fully extracted by rocket engine and used to accelerate the rocket.
On the other hand, work made by rocket engine goes to increase kinetic energy of both the rocket and remaining fuel still moving with the rocket. So in a rocket you essentially push some energy in fuel first, then recover some of that energy back via rocket engine. You always put 100% of energy in fuel, but can recover only a fraction of that back and your formula is actually saying how much energy would be recovered.
There are some practical effects that come out of this observation. For example, consider a car with a 200 hp engine. Even if you drop all friction, air resistance, etc., the faster the car go, the slower would be its acceleration. This happens because energy of a car grows linearly with time and kinetic energy is proportional to speed squared, so you have to do more and more work to get one extra mile per hour. But thanks to that "extra-energy-in-fuel effect" this does not affect rockets. In fact rockets will accelerate faster and faster as the time goes, despite rocket engine nominally having the constant power much like an engine in a car. This happens because there's more and more kinetic energy available in rocket fuel and with decreasing amount of fuel in rocket, less and less energy is going there.
Normally you don't really need to think about all this, because there are equations that are much more practical for actual rocketry. However there's one nice trick called Oberth effect that really capitalizes on this idea and is actually used in space exploration. In Oberth maneuver one uses planet gravitation to accelerate the spacecraft and fuel inside it, getting some extra kinetic energy in that fuel. Once spacecraft "collected" as much kinetic energy as possible rocket engine can be fired to extract useful work from it. And it actually works.