"Don't you need to sample both the voltage and the current simultaneously and integrate their product over time to get real power? "
Definitely - With just a current measurement a single device estimation for power is not going to be very accurate due to Power factor - Wikipedia as well as voltage not necessarily staying constant.
I've added another section to discuss accuracy of this system as well as some trials using different single devices. I've also switched from simply using the peak value off of the CT to an RMS calculation.