Unless a stove has a shut off valve, it is considered an open fire. So, the Bush Buddy would be considered an open fire. Along the JMT, wood fires are not allowed above 10,000 to 10,500 ft depending on where you are. This is to protect the sparse living and dead trees from being burned. I fear that your Bush Buddy would be viewed as an open wood fire by the agencies that manage the trail
I suspect that if the USFS or NPS were required to take official notice, Esbit and alcohol stoves, lacking shut-off valves, would have to be considered open fires and subject to fire regulations. But, since they leave the wood resource untouched, I don't think they are subject to the "No Wood Fires" regulations. I have certainly seen a lot of alcohol stoves used on the JMT above 10,000 ft but no Bush Buddies.