The claims are pretty amazing. High efficiency, efficient over a wide range of temperature difference, high temperature differences possible.
The operating principle is totally different. It is based on acoustic waves. Not using phase-changes but just the ideal gas law (pressure and temperature are proportional). I tried to get my head around it, and I got it with a standing sound wave. But they use a traveling wave, for which I could not find explanations I understood.
The general idea is "lower air pressure and move gas to cold side so the gas heats up" followed by "raise air pressure and move gas to warm side so the gas cools down". That means the low pressure needs to be low enough that the gas gets colder than the cold side, and the high pressure needs to be high enough that the gas gets hotter than the hot side. Luckily that is 'just' a matter of amplitude of the sound wave. I think this is how they achieve their wide range of efficient temperature deltas.
That wide range is the main difference with a phase-change based unit. The phase change happens at a much more difficult to change temperature.