[RedDevil]

Let's put it this way. It is not a trick, nobody is cheating.
Once you see it there's no way back; I was thrilled and all I wanted to do is share what I found.

The spool is relevant because it is the same principle of feedback loop.
It is the EGR valve of physics.

What makes this problem hard is that we mentally seek a frame of reference, and if you take the car or the ground as a base it is quite difficult to see how the forces act.
But if you take the surface of the blades it is actually quite simple; just like the rope on the axle of the cart it moves slower than the wind (or cart) AND it is the main surface the wind acts on.

If you are still sceptic, please do check the following:

Step 1.
Imagine a car with a propeller that does not turn at all.
The wind blows against the propeller like a sail and the car moves forward.

Step 2.
Imagine a car with a propeller driven by gearing. However, the blades are set flat so their turning does not have an effect at all.
The wind blows against the turning propeller and the car moves forward.

Step 3.
Like step 2 but now we set the gearing such that the blades are slanted lightly. The blades would push the air backwards, but do so more slowly than the car moves itself.
The wind blows against the turning propeller and the car moves forward.

Step 4.
Now suppose the car in step 3 moves as fast as the wind.
The body of the car endures no force at all from the wind. But the propeller does, because it is turning slowly against the wind. therefore there is a resulting forward force.
Of course there is also a force that fights the rotation of the propeller but because of the gearing and blade angle, that force is smaller than the forward force.
After all the angle is such that the surface the blades present still moves forward, albeit slower than the car itself (and of course slower than the wind).

The car is moving at the same speed as the wind, so no energy can be transferred to the car.
The surface of the propeller however moves slower than the wind, so the wind can transfer energy to that. And there's the ground which of course moves relative to the car and wind; this is essential to grip the wheels to drive the propeller.

Step 5.
For reference we increase the angle of the blades so that it would push the air backwards faster than the car moves.
Now when the wind blows against the propeller the forward force is less than the force fighting the rotation. In fact, it will rotate the other way pulling the car back against the wind.