Well, it's a electric assisted bike... common nick for such bikes is Pedelec.
Thing is, they did go to the extreme and fit lots of cells and a powerfull motor.

The video was shot in Monaco, explaining the luxury all around... The bike itself is a whoping 12 000€ (mainly cells I guess...)

Another angle where you see the guy pedaling... and more peaceful ride in Berlin.
http://www.youtube.com/watch?v=tzsHF...layer_embedded

Regarding road legal issues?
The second vid shows the thing is equiped like a moped... and I guess should be like a 125cm3

In Europe, that would be considered a pedelec only if it is a bike, the electric motor is 250W or lower, electric assistance stops at 25km/h.

then you have mopeds, no need for motorbike driving liscence, but you need a motorbike helmet, insurance, vehicule lights, number plate... but you're limited to 45km/h

Next step is a light motorbike driving liscence, up to 125cm3 for petrol engines. I do not know for other types. But that bike would fit in that category. So you need plates, insurance, motorbike helmet, vehicule lights etc...

This is not your average bicycle, isn't it?