Does it count if you don't leave the airport?

Later today I'm flying to Dallas for a board meeting for my current job. The meeting will be held in the airport. Not just at one of those attached airport hotels, mind you - in the airport itself, in one of those special clubs that airlines have for super-duper-frequent flyers. I've never been inside of one before, myself; just caught glimpses, cool and inviting and mysterious behind frosted sliding-glass doors.

I'm flying out a day early and will actually stay in a hotel 5 minutes outside the airport itself. But lots of other people are literally flying in just for the meeting. My boss who's here in Seattle is doing that, flying in tomorrow morning, attending the 5-hour meeting and flying home. It's a 3+ hour flight each way. What a long frickin' work day that makes.

I just find this concept kind of odd. So those people - and even ones coming in a night ahead but staying at an attached hotel airport - will essentially never leave the airport for the entire trip. Does that count? Do you ever really arrive in Dallas in that case, or are you suspended in a kind of geographic limbo?