Unfortunately the explanation of the A/C fluid cycle is haphazard and the description of how forces relate to crankshaft position is completely wrong. The crankshaft actually applies maximum force to the piston while approaching top and bottom dead center, when the mechanical advantage is greatest, and the least at mid stroke, where the torque of the motor is most directly opposed by the pressure of the gas against the face of the piston. This is good, however, because it marries well to the available power through an alternating current system.

The design described does seem to have fewer moving parts, which is good. But the advantage of linear vs rotary motion with respect to forces seems sketchy. Field strength in the linear system is likely to vary across the travel and would still need to be synchronized to the alternating current to prevent motor stalls. (Edit 50 of this comment: this effect is actually illustrated directly in the video here: https://youtu.be/2TFiL5BM3ss?t=348 Imagine the field lines directly correlate with force applied, and mentally plot the quantity of field lines over time as you watch the animation. Turns out it looks precisely like the force chart of a rotary compressor.)

The primary advantage of this pump, to me, seems to be reduced weight/complexity and lower friction losses. For it to operate with low starting load it would likely need to essentially vibrate its way to full travel (confirmed at 7:47 in the video), something rotary compressors can’t really do. If you try to restart rotary compressors too quickly after stopping, the high head pressure will stall the motor. This causes it to effectively be a dead short minus winding resistance, pulling much more current than average (known as LRA or locked rotor amps) with no cooling. This will heat the motor quickly until it thermally trips or burns up. This is why you will frequently see restart delays in A/C systems.

For what its worth, scroll compressors have been around forever and share some of these advantages, but aren’t dominant in the industry because of the additional complexity in manufacturing. They have an additional advantage of somewhat continous output pressure, which *significantly* reduces ambient noise and vibration. They also have fewer moving parts and are generally more reliable.

All of these advantages convey to standard air compressors by the way, something I'm a little surprised they didn't mention.