I will hold off judging till I see (a lot) more information but at the outset it is hard to understand how they can possibly work. The fundamental problem is that although a person's hearing will almost never measure a perfect 0dB across both ears during an audiogram test, the brain will compensate. So that despite any measureable shortcomings in that person's hearing, it is what it is. In other words, their theoretically flawed hearing still sounds "normal" to them because of the way the brain compensates. This is why recordings that I have owned for the last 40 years sound exactly the same to me now as they did when I was a teenager. So if these headphones, for example, were to compensate their output so as to result in a theoretically "flat" response, they won't sound right - they will likely sound way too aggressive. Apart from that, most headphones don't sound remotely like a speaker in a room does anyway and for me, natural sound means what you get sitting in a properly treated room when the sound source is some distance away. The room effect and the distance will considerably effect the frequency response. So all of that being said, I have great difficultly understanding how these could sound remotely natural.
I can understand how a concept like this could work for people with significant hearing deficits (for example, they require hearing aids all the time), but not for a "normal" person even though that person will likely exhibit measureable deterioration (whilst being within the measured boundaries of "normal" for their age).