The wheels start moving.
The wheels start moving the blades in the rear.
There is no air, but the propeller creates forward momentum.
Obviously they cannot accomplish without moving the wheels, the wheels provide the movement to the props, then the props provide forward momentum to the wheels.
Its a cycle.
Yes, sure...but you can't create more energy than there was to begin with. The treadmill is providing the power (a fixed amount of power) to the prop through the wheels. Somehow, the cart outruns the treadmill and maintains that constant state ability (shown by the strings pulling forward). Once the strings pull forward, the cart shouldn't be drawing any more energy from the treadmill because it is now pushing against the belt underneath. The treadmill is effectively not putting any more power in the cart since the cart is now pulling forward.
If you consider this example on an open road instead of the treadmill, this video seems to show that once you got that little cart up to a certain speed that it would accelerate and maintain some set speed on it's own without any energy input...which should be impossible.
Maybe, if there is a little angle between the tied/fixed direction of the cart and the treadmill, the wheels could turn faster than the treadmill is moving under it and some additional energy could be derived from that - but it looks pretty straight.