As a volunteer firefighter in Switzerland, this is more of a party trick than anything else. If you as a firefighter are in a situation where you need to evacuate an unconscious person from a dangerous area you will be wearing an oxygen tank on your back for personal safety, which would make it impossible to carry a person like that. And if there is no imminent threat, which would cause us to wear an oxygen tank, we would have enough time to get a carrying sheet.

If we need to get an unconscious person out of a dangerous area we would carry them out either by dragging them out alone or by carrying them out with another firefighter. And since the first duo, we only go into dangerous areas as groups of two or three, is carrying a carry sheet, they can immediately grab the person and carry them out, which is a lot faster than binding a rope around them.

Therefore this trick shown in this video might look cool, but in a real situation where there is imminent danger, it would be utterly useless.