Hi , Really interesting and cool,
Yes this is totally possible ,and should work .
as the subject says Mess with your mind . there are 4 forces all working together here . Plus the fan is not just a propeller .
This experiment just would not work on a tread mill as in real life they ran it on a very large flat open surface without opticals .
The bit were the fan started wobbling but as the wind increased it stop .. this is caused by fan tip speeds and centrifugal force which in turn stabilizes
the craft and the tip air flow will be faster than wind speed . So when all the forces balance it will travel faster .
These guys really went to the next level .

Yes it seems it messes with many peoples mind.
What do you mean by the fan is not just a propeller ?
The experiment worked perfectly fine on a treadmill see the propeller based cart showing as moving forward on a treadmill.
The Fan is not just a Propeller as it has several functions in this type of setup . I was sorry that they did not use a smoker to show how the air was moving.
the wind is turning the fan . that is connected to the drive wheels . that energy move it forward . the fan/Propeller starts to spin faster . The tips of the propeller
are now creating a rotating vortex . Screw effect . so the air to the side of the vortex will move outwards > So the when equilibrium is reached the front
should have a lower air pressure . less resistance (vacuum) the propeller is now blowing the craft . Yes there is ground resistance but it gets faster the
propeller will try to tilt back and will stay . More like a gyroscope would Ballance.
I see how this works but find it hard to explain exactly why .
The experiment worked perfectly fine on a treadmill see the propeller based cart showing as moving forward on a treadmill.
Yes I saw that experiment with a small model and a good wind source but it needs the distance to get all forces balanced very hard .
Update whats with the treadmill . this is thinking back 100years when people thought if a Car went faster than 7mph you would get sucked out
I totally agree that they should use something like smoke or a small thread on a pole to indicate air movement for the experiment on the treadmill.
This would show that when at the speed of the wind (e.g. whicle stand still on the picture) the prop is pushing the air against the direction of the belt of the treadmill. So the wheels are powering the prop, and not the other way around. This is the main point for the understanding.
There is no need to include complications like a vortex around the prop, just consider the prop as a way to drive the vehicle relative to the air and generate thrust. To make the vehicle go forward the porp has to generate a little more forward force than the wheels generate backward force when they generate the power for the fan. The technical difficulty is getting the fan to produce enough thrust with the given power. So while the principle is simple, getting the prop at the right speed and pitch is not so much.
....
What do you think will power the vehicle after the wind speed is exceeded ? As wind can no longer power the vehicle that travels in the exact same direction?
The wind can not longer power the prop, when the vehicle goes faster than the wind. However the wind can still power the vehicle. This is the special effect shown here.
When looking in the reference frame of the vehicle (or wind when at the same speed), the prop takes energy from the wheels and blows air forward against the wind.
When looking in the reference frame of the ground, the prop takes energy from the wheels and as it produces thrust (asignst the wind) it also absorbes power from the wind. If designed well the power absorbed from the wind can be larger than the power needed to drive the fan.