Note how the wheel steering linkage (arm) has been disconnected:
The wheel freedom is limited to about 80°, the arm must be disconnected in order to go further. In this video, while this disconnection is neither shown nor commented, you can see the arm connected at 0:43 and disconnected a second later.
This 80° limit is for a good reason:
You can see only one tire would touch the ground at 90°. The wheel actually stands on the tug platform, the tug supports the aircraft weight while turning.
Note how the lower part of the wheel jack has turned, but the upper part didn't. The disconnected arm moves with the wheel, but the arm anchor points position hasn't changed. They are in the position last commanded from the cockpit.
Details of the cradle and turntable from Lektro:
The operator disconnects the arm, hooks the wheel with the yellow U-hook, moves the wheel onto the turntable and locks it by retracting the hook with the flat strap.