Do you agree air is a compressible gas ?
Yes, but I don't think it's relevant. Without air there would be no puzzle since there would be no wind to move faster than

I think the crux of it is that you're missing the effect of the wall of air. That wall could be a moving sail, being pushed back by the vehicle, except that there is a finite distance to which it could be pushed. With air, there is no limit because there is always air in front of you to push back. There is no infinite mechanism to do the same for a sail.
But let's assume for the moment that it is a sail, and the vehicle is infinitely long. The sail starts at the front and moves backwards at 1ms, say. There is a wind pushing the vehicle at 2ms. But that's pushing against the sail, so the wheel speed across the ground is actually 3ms - the 2ms wind plus 1ms sail.
That's how it works. The vehicle speed across ground is the wind speed plus the prop wash speed. Simple as that.
Ah, but the prop is powered by the wheels. Which is fine because the real vehicle speed will never reach the theoretical maximum. As has already been discussed, as the max is approached the wind power drops off and the speed stops increasing. So, in our example above, the vehicle may be doing 2.5m/s and can't go faster because of the lack of power as the vehicle-prop velocity approaches wind speed. But, as also noted, as the vehicle speed drops the apparent wind power will increase. Given the available wind power (acting against the diameter of the prop wash) is greater than the frictional losses of pushing the wheels to turn the prop, the realised speed can be higher than the winds ground speed (which is what all this is about).