Things that cool and heat *effectively* require more power than you may think. I've seen 12v coffee makers, which, seem 'efficient' and handy, but what most people report is that the coffee takes a long time and isn't very hot.
If the comparison is of any value, the typical electric RV fridge needs about 350w. That's a lot to ask of a single 12v battery, which is why propane is a better option. Yes, I'm aware the cooler is smaller.
So, if that Dometic box really does use so little current, I'd be at least a bit skeptical of its cooling ability.