I don't know how much of a problem carbon dioxide would be from this. Some fuels pose a more serious problem than others. Oil lamps and candles are used indoors all the time.
While ventilation is always good for any flame, the amount of carbon dioxide produced from one of these does not displace enough oxygen to be dangerous. Even in a small apartment. I wouldn't recommend one of these in a tent, not because of the carbon dioxide issue, but because I'd never light a flame in a tent and risk burning or melting the tent. It's always important to be as safe as possible, so thanks for raising the issue.
Although you state there is no smoke from the emergency heater, you have not addressed the problem with carbon dioxide which could kill the family. There must be a fresh air source and proper ventilation. Boy Scouts are taught that you can not use open flame heat sources even in a tent.
I am worried enough about carbon monoxide poisoning that I tried this in the kitchen under mild emergency situation. Mid 50's outside, no wind. The co2 alarm went off after 5 minutes. The heater did not warm enough to make a difference in comfort in the room. It is not a good idea to use this in the enclosed areas most people will use such as a bedroom, bathroom, etc. Also if it becomes upset the liquid fuel will turn a room into a furnace in seconds, and with most cloth products made from plastics, the outgassing from burning will be deadly. Please take this video down.
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