On a theoretical level, food calories represent a specific amount of energy that can be extracted from food. So some kind of calculation could probably be made as to how much work is required to operate the exercise bike, which probably depends on your height and weight. That work uses a certain amount of energy, which is probably equated into calories.

All that said, I have no idea how accurate that would be. And in the end IIRC there’s a bunch of other factors that affect how humans burn calories and gain or lose weight, so in the end the calorie burning stats only really need to be comparable to other calorie burning stats. So I think the bigger question is: Do different exercise equipment types put out comparable numbers?