Using an ecclesiastical candle snuffer on my birthday cake

In these Covid days, we decided blowing out the candles might be deemed risky so I was handed an ecclesiastical candle snuffer. It's an open system in that air can move freely in and out of the bottom if the cone if it wants to, so why does the candle go out? The candle's combustion reaction turns oxygen into carbon dioxide. This is warmer than the air outside due to combustion so it tries to rise upwards. A normal fire has a chimney so it can escape upwards and draw colder oxygen-rich air in at the base. That can't happen here because the rising air is trapped. It's pressure must be such that air cannot move up. Since it is warmer, it is also likely to have a higher pressure as well which in theory would tend to drive some of it downwards. Not sure if it really is hot enough for that.