Two minute promotional video for SkiClaws FC created by Brendan Preston Productions, Whitehorse, January 2021.
Kick with one foot, glide with the other, much like on a skateboard, scooter or kicksled. It can be useful on level ground, shallow grades, when wanting quick acceleration, or for powering up short hills. It is the fastest cross-country skiing technique in icy conditions. (video courtesy Mponda Kalunga, 28 Feb 2021)

The crowdfunding video is the most recent and best. If you are interested in ancient history, look farther below.

The animations (thanks Quantum Lee) are of prototype 3.0. The cell phone movies are of two prototypes. The first three are of prototype 5 from March 2017 (thanks to Andy and Joseph), and the others from the clunkier 3.1 (thanks to Beanster).
Below is an animation of the principle in action.

With the animation below, click the pause button then move the slider. This shows an exploding view of the parts. Note that the lower pivot point of the claws is on a plate mounted to the top of the ski. The sidewalls are not affected.

Here are three March 2017 videos of prototype 5. The first shows a skier approaching a hill, ascending, and continuing on, all without stopping. The approach uses the skateboard or scooter technique, the ascent uses alternate steps, and the departure is again skateboard style. The skis have factory bases that have never been waxed.

This video shows the same hill (previously well-packed by herringboners) with focus on the feet.

The last March 2017 footage shows the feet and the skateboard technique on level ground.

The next three videos are from early 2016 with prototype 3.1. The first shows the basic means of engaging and disengaging the traction device.

The next shows the skateboarding technique on level ground. The surface is extremely rough. The engaging motion is highly exaggerated (director’s call).

The next movie demonstrates uphill technique with SkiClaws prototype 3.1 on extremely rough snow. At the beginning, the skier is able to jog a few steps, then the steepness and roughness of the slope cause him to slow. The skis had never been waxed in any fashion.