An rv frig is different than the one found in a home kitchen. It cools via a chemical process vs. one that requires a compressor (and the associated power to run a compressor). The A/C in an RV "does" have a compressor that requires a large amount of AC current to run.
The only power needed in an RV frig is that required to boil the liquid that starts the chemical process. That heat requirement is easily supplied by either propane or electric. Some RV frig's will be OK with AC or DC to supply the heat to boil the liquid -- or, propane.
The gas condensing cooling system that the fridge uses simply cannot provide enough cooling (btus) to chill a large volume of air quickly enough to be useful for air conditioning. The gaseous condensing unit would have to be huge to get 13,500 btus of cooling.