I just spoke with "Diane" (Staff, Not a volunteer) at the RMNP Information Office.
I asked about an "alcohol stove", explained as a "short can with burning alcohol in it, with the cooking pot suspended above", with no capability to turn it off. I also offered that the Fire Ban in my county requires fueled stoves to have an on/off valve.
She offered to check and call me back. And she did. And said that stove was allowed.
So, IF you take an alcohol stove into the back country, I would also take the full name and phone number of your RMNP contact. Because confusion is rampant.
[And do be careful. A few weeks ago a camper in northern Colorado knocked over his alcohol stove and did, literally, set the forest on fire. The Hewlett Fire burned 7,685 acres, engaging 370 firefighters and three helicopters, cost $3.2 million.]