Cool. regular shocks absorb - these look like they store and return, so probably do not rob energy from the rider?
You guys should find a short rocky downhill slope, free-wheel down it, and see how much further these things roll out at the end, than a regular shock.

"It has no moving parts". Explains why it doesn't work all that well. Still, the parallelogram method of keeping the wheel in alignment is a good start.

It has no moving parts but has 60mm of travel. Correct me if I'm wrong but you've got to have moving parts to get any kind of travel.
The only way I can see fork being marketed with no moving parts is if the springers and springstacks are sold as a separate unit as part of the hub on the wheel.

"Correct me if I'm wrong but you've got to have moving parts to get any kind of travel."
Nope - material flex isn't a "moving part".
The idea of flex as suspension isn't new - "softail" mountain bikes have relied on inherent flex in the frame for years, admittedly usually in "pivotless" designs, with the actual shock-absorption being provided by a small shock or elastomer, and flex in the (often flattened) chainstays replacing bearing pivots.
Cannondale's Speed Save technology relies entirely on flex, however.
Having some small experience of carbon fibre as a material, I'd prefer Lauf to use titanium plates rather than carbon fibre - titanium doesn't fail catastophically the way carbon fibre is wont to do...

Motorcycles had similar arrangements,I say similar as I'm unsure about the parallelogram set up, but leading link and trailing link forks were very common in the 50s and 60s and even the humble Honda 50 step through had a similar suspension. Rubber bushes held in torsion were often the "spring" of choice in the past .

To really save weight, spring-pivots can be used in many designs right in the primary load path, instead of making a detour. The Hossack system of suspending the steering head might save even more weight. With this much travel, dampers become more necessary. They are harder to integrate. They also rob power, though not as much as bouncing with no springs. A rising-rate spring needs less damping, and a friction "shock" with a soft mounting ignores the little stuff. To avoid pogo-ing, a spring fork should be matched to a rear suspension with extreme anti-squat geometry, so the bike only rises and falls with no pitch from pedal reactions. @Martin H. : "moving parts" is usually taken to mean "with pivots." Everything moves as a spring, on close examination.

In this design I see the springs. But no dampers.
The damper is the "absorber" part of the "shock absorber". You really need that part. Spring only = bouncy bouncy crash bang ouchee.

As others have stated... No damping! If you want an innovative spring design then this is for you. If you need rebound and compression damping... well then you'll need a few moving parts.

I've always preferred linkage forks. I have a Lawwill, a Girvin and an AMP (all of the last of the series). They are inherently limited in the amount of travel but are much more stable against side deflection (imho). All of the aforementioned have dampers.

So "moving parts" is usually taken to mean "with pivots". So a regular shock would not be a moving part? A ball bearing used as a check valve would not be a moving part? A cut off sled on a table saw would not be a moving part? Perhaps no surface to surface motion would be a little better.