Something's wrong here (possibly my understanding). A major online retailer lists replacement batteries for a Galaxy S5 rated at 2800mAh. This is 10,800 coulombs. To transfer that amount of charge in 30 seconds would require over 300 amps. I don't want to be standing nearby.
TAIYO YUDEN has had a Lithium Ion Capacitors on the market since 2010.
3.8V @ 270F from distribution is about $60 each.
Hopefully these newer ones will have more realistic pricing, if they ever reach production (Seems few of these announced products ever do. When can I buy my first Graphene based anything from distribution for example?).
I too was initially puzzled, but what they seem to be saying is that you would make a battery from this that could accept charge much faster than conventional batteries.
Currently the thing limiting the charge rate is how fast the chemicals in the battery can recombine. This seems to behave more like a capacitor.
Is the voltage relatively stable over the discharge range like a battery or drooping at a exponential rate? That I don't know, but I think there may be limits as to how quickly you can draw from the grid creating a substantial market for intermediate storage as well.