Well then, yet another "we will fool you with video magic" hoax theories that most people aren't capable of explaining or understanding.
Who am I to utter such an opinion? I'm an electronics experimenter, a radio amateur - and a service technician for many years for Commodore Computers back in time, if you need further info - I'll reveal my youtube channel ;)
Anyway...this is just a hoax. It's a neat theory - but a hoax nonetheless.
Why? Because a few spirals like that without receiving any inductive power of any significant signal strenght simply isn't feasible. The spirals drawn in the image with conductive ink is supposed to be coils that will oscillate at a theoretical frequency, and the shape of each will give each "wireless" button an unique identity.
Well - guess what, that technology is already in use in various anti-theft alarm devices (RFID tags) on clothes, true - these particular tags doesn't use any batteries - but they're depending on inductivity and will react on resonant frequencies. You don't even need a chip for this, just an unique resonant design that can be read with the corresponding frequencies that the receiver receives.
What the people in the video probably did in order to demo this, was either very simple (a few small touch sensitive buttons BEHIND the paper with the conductive ink) connected to an USB keyboard that has been taken appart and wires connected to the corresponding buttons under the paper (as you can see, they reveal nothing, but take great care to cover as much of the screen as they can when they demo this, and don't go out of their way to show you EVERYTHING. They could do this - but it would require far too much video editing. ;)
Another way to do this - would be to use some standard NPN transistors and use them as a "switch", you can use that by properly biasing the transistor so the B (base) becomes so sensitive that it will let power trough C (Collector) and E (Emitter), the touch works because you'll most likely have MAINS nearby that emit small electromagnetic current signals (the 50/60 HZ humming you hear in your amplifier when you touch the input/aux terminals).
Same thing. Easy to fool the viewers this way.
In fact, Bang & Olufsen were one of the first stereos on the market to implement TOUCH based buttons using this very same technology (touch buttons with sensitive transistor B (base) inputs...
Try again boys!