I noticed that the end opposite of the HDMI seemed to have a micro USB in port on it. I suspect that it is powered via that, however none of the demonstrations showed it being plugged in, so I believe it may have an internal battery which needs recharging.
Edit: The specs at the bottom of the page don't list a battery but it does list an included power adapter, so I guess you have to have that plugged in at all times.
Edit 2: Certain versions[1] of the HDMI spec provide power. It's possible that the USB is a backup solution for older spec'd TVs.
The Gamestick is powered by MHL if you have it, but you have to power it through its micro-usb port if you have normal HDMI (source: have one). I expect it's the same for the Chromecast.
Edit: The specs at the bottom of the page don't list a battery but it does list an included power adapter, so I guess you have to have that plugged in at all times.
Edit 2: Certain versions[1] of the HDMI spec provide power. It's possible that the USB is a backup solution for older spec'd TVs.
[1] http://en.wikipedia.org/wiki/Mobile_High-Definition_Link#Fea...