Good review with plenty of good points raised. However, their medical expert failed to mention a basic point about air delivery. When we are breathing quietly, we inhale about 500mL of air in just under a second. This means that the air delivery system needs to instantaneously supply 30L/min when we inhale. If we breathe 14 times a minute, that's less than 14 seconds where the high flow rate is required, and the rest of the time the fan is working for nothing. For context, the Dyson hair dryer supplies 40L/min and that is mains powered and makes a lot of noise. I was unable to find the flow rate of the headphone, but I doubt if it is anything close to 30L/min because it would very quickly dry out your nostrils, mouth, and eyes. Not to mention, it would be pretty unpleasant if it was winter and it was blowing cold air at your face since it would strip off the boundary layer of air on top of your skin and increase evaporation (see
wet bulb temperature) and make you feel even colder.
IF it is unable to supply the required flow rate ... well, the unit is not sealed so you breathe in unfiltered air from the environment. What this means is: at best, maybe the first 100mL of your 500mL breath will be purified air. All this depends on the flow rate, which I don't know because the specs aren't published. The rest of it will be regular, unfiltered air.
TL, DR: they won't work, and they don't have a hope of working.