How much should it cost to run a gas fireplace?

It's probably not so much the fireplace that's malfunctioning (otherwise, where would so much gas go?) but a combination of factors, chief among them probably being - if they have time to use the fireplace, then they are staying home and want to be warm. So the main furnace is likely being cranked up during those times as well. I imagine your average Airbnb guest does not stay home all that much, only at night, so the heating gets used less in general.

Additionally, a running fireplace creates extra drafts in the house, thus actually cooling the rest of the house, and making the main furnace work harder. In fact, I believe Myth busters had an episode about exactly that.