Your watch battery isn't small. This battery is small. At six times thinner than a bacterium, Rice University's new battery is 60,000 times smaller than a AAA battery.
The immediate uses for such a battery would be in medical tech, helping to power implantable medical devices and nanotech. They could also power microscopic wireless networks or any other tiny, embedded computers. Really, once the tech is finalized, the possibilities are endless. After all, you're not gonna have nanotech robots without a way to power them. Now we're halfway there.