The caption does say power density, but it quotes an energy density of 4200 mAh/g. I suspect that whoever wrote the caption isn't an engineer or physicist.
I predict that there will still be people who have difficulty keeping their cell phone charged :-)
I agree with you, plus I don't understand how energy density is increased 10x with low resistance wire, seems like that would help more on peak power (or the carbon solution is really realy crappy eating up to 90% of total energy. If it is power, then the benefits are much more limited. Hmmm!