One of their cofounders has several published papers, patent applications, and such that sound like they give more details on some of the underlying science and technology. There's a list here: http://scholar.google.com/citations?sortby=pubdate&hl=en&use...
Oh thank you very much for that. Wow, that "Bioorganic nanodots for non-volatile Memory Devices"[1] is a pretty quick read. I'd bet money they have used their material to build what is effectively a high internal resistance capacitor, storing charge rather than a chemical process. That makes much more sense as charge storage is limited only by dielectric constant and the internal resistance.
To make their video compelling they need to then start a program on the phone, and show it and a clock before the 'low battery' alert goes off. That will give a sense of how many watt-seconds they can hold in that volume.
