Yes it is a millivolt thermostat. The electricity to run it is generated by the thermocouple in the pilot flame. (Like gotpasswords said)
So why doesn’t the furnace work when the power is out?
It does work when the electricity is out.
That’s not what foolsguinea said (bolding mine):
Without seeing the furnace in question,I can only assume that when the coal-fired gravity furnace was converted to gas, they kept the existing electric-powered controls - just a WAG, but the coal furnace probably had an electric-powered stoker to feed in the coal. Electricity was already there, so they didn’t change it.
Could they have done a full conversion to gas and a millivolt control system? Certainly. It just sounds like they didn’t.
IME, millivolt thermostat loops can be a bit fussy (less than reliable). While it is bad to have a furnace that doesn’t work due to a power outage, it isn’t much better to have one that quits for no apparent reason at all.
We have two wall furnaces with millivolt controls. Having two of them provides some redundancy, which is needed. In the last five years I have gone through three generators* and two thermostats to keep them working. If there were only one of them, I would probably have replaced it by now.
*Millivolt thermostats use special high output thermocouples which are known as generators to distinguish them from the smaller thermocouples used as flame sensors on 24V controlled furnaces.
I had an ancient millivolt system in my last house. One cold winter’s evening I was wallpapering the dining room. I cut the power to that room to work around the electrical outlets. It turned out that the furnace fan was on the same circuit (weird wiring, one of the many treats of old houses!). The furnace kicked on, then kicked off a minute later. There was a burning smell.
Turns out the current generated by the pilot light was enough to give the “turn on” signal to the furnace, but without electricity to the fan, the heat wasn’t distributed properly. It fried a different thermocouple in the furnace (hence the burning smell). The overheat sensor kicked the furnace off. (fortunately) When we realized what happened and turned the power back on, the darned thing still wasn’t working right (due to the other fried thermocouple). Of course this happened on a Sunday evening, which meant expensive service call by furnace repair man to get new thermocouple. Which didn’t work right, which meant a repeat service call the next day.
Further research taught me that such systems are no longer kosher - there should have been a mechanism in place (other than the overheat sensor) that kept the burners from lighting without a fan to disperse the heat. (the very same feature which disgruntles the OP) We are lucky we only fried a thermocouple and not the whole house.