That wave-shaped mark is characteristic of rotation. Imagine the aircraft turning around the center, and that nose gear trail as its relative position moves around the center of rotation.
Imagine a spinning car sliding down the road. The center of rotation is the center of the car. As the car spins, the tires are rotating around the center of the car.
As you look at the skids, they leave a mark like a sine wave, but the vehicle was moving is a straight line and rotating.
Another thing, with the landing gear gone (like a car with the wheels locked up or that is on its roof), a rotating body will continue to rotate in the same direction unless it strikes something that changes its rotational moment.
With no rudder and no gear, and on a smooth runway, it is highly unlikely that the aircraft yawed, cancelled the rotational energy and then began rotating in the other direction, then cancelled that energy and began accelerating back the other direction.
An aircraft with a functioning tail and intact landing gear might, possibly, be able to accomplish that. But this aircraft was not.
Edit: Were's a good video of a car spinning out with visible skid marks. If you watch it, try to isolate one wheel, and see what that skid would look like by itself.
http://www.youtube.com/watch?v=XwlPe2to548