I haven't researched this fan, but my suspicion is that it's similar to an "anti-gravity" device that showed up on Mythbusters a while back. They built theirs out of aluminum foil, wire, and maybe a little balsa wood, and when a current was applied to the device it hovered by inducing airflow and creating thrust. This appears to be doing much the same thing.
Sure, it gets rid of that noisy air impeller, but before one declares air impellers to be worthless it's worth recalling why we've used them for so long. Prop fans are simple and effective, although they can't handle much static pressure (a weakness that I wouldn't be surprised if this device also had). There are lots of other fan types, many of them quieter than prop fans, that can efficiently move air. I'd love to be able to have a completely quiet fan with no rotating parts for some of the projects I design, but if this thing works the way I think it does, it strikes me mostly as a novelty.
