ANY time there is a wireless transmission of data, there is a transmission of power. The only difference in this case is that they are transmitting a signal with a much larger power output and (hopefully) concentrating the direction of it.
Your routers (most of them anyway) might be transmitting a total of about 1 mW about equally in every direction. When your wireless card picks up the signal, the antenna is receiving a signal in the order of micro or nanowatts (because it only picks up from one point in the "sphere" of radiated power), and then amplifying it in order to decode the data.
If your router didn't radiate any power, there would be no signal to pick up.
We may or may not ever see a device like this in our homes, but there are some applications -- I'm thinking mainly military-style devices/vehicles where they can't afford the weight of wires to transmit power, but they can afford the wasted power.