the little LP fridge in my camper uses 1300btu for cooling, takes a good 6hrs to get down to normal fridge temp and duty cycle on the burner varies wildly with outdoor temp and how often you open the door, might be 100% one day and 30% the next, standing pilot is always lit. Your newish fridge should use less than 1kw per day if you aren't leaving the door open all the time. If it's a decent fridge it uses less than $60/yr at $0.11/kw. For comparison a NG fridge will use around $35/yr in gas assuming a 30% duty cycle on the burner, in reality it'll probably be a wash overall in running cost.
For an appliance that is likely to last less than 10 years I'd go with an electric model all day every day, cheaper to purchase, cheaper to install, cheaper to replace, widely available, relatively easy to fix the common problems.
Gas fridge, very expensive to purchase/replace, expensive to install (need a gas line), very expensive to repair ($1100-3500 for a chiller unit vs $350 for a compressor), hard to find, definitely not going to get one at home depot or menards.