Honestly I think you need to take responsibility for yourself. You should have made sure that you had ample amount of time to get to the airport in time for your flight. Either your pick up time was cutting it too close to your take off time, or magical express was running very very behind. Either way, you should have complained to the front desk or someone in the hotel as soon as you realized the error. If your time was cutting it too close you should have requested an earlier pickup time. Or if the shuttle was more than 15 minutes late, you should have gone in and found out then what was going on.
Once you realize there's going to be stops at other resorts, did you ask the driver how many more stops? Or how much longer it would take before you left for the airport? I think at the point that they were already late and then making additional stops, I probably would have gone in and complained at whatever resort you were at and asked someone to get me a taxi/towncar and request they pay for it. If they refused I still would have taken a cab and fought them on that later. But if you never alert them to the problem...
Although I think that they should help you in securing another flight and using whatever resources they have, I don't think that they should be financially responsible for your missed flight.