Some former neighbors of mine had a gas air conditioning unit. It required electricity to operate too but mainly it ran on natural gas. I wish I had one, don’t know if it is even possible any more, the electric company has their hooks into us now.
I remember the refrigerator you posted, I remember when we had one but I didn’t know they ran on gas.
RV’s today use the same principle in their refrigerators only there is generally 3 ways to run them. 110 volt AC current, 12 volt DC current and propane. Propane is the same principle as your pictured fridge. A small pilot size flame is all that is needed and it changes the refrigerant from a liquid to a gas which is where the cooling effect takes place. Instead of R-22 freon it uses amonia, very corrosive and is generally the reason you don’t see house size AC anymore. The units for houses were quite large to provide enough cooling for a house also.
Decades ago the local gas companies tried marketing the units but gave up because of size and corrosive amonia.
Probably similar to the technology in a electric/propane fridge in an RV.