Closed loop. Each owes same amount to the next in the chain = net 0 debt.
Always works if the chain is closed.
Yes, that's how I saw it too. The town actually had a net debt of zero to begin with. Each person owed another $100, but was in turn owed $100.
It would have worked exactly the same if there was no tourist and the hotel owner simply paid the next in line $100 from his till. The $100 would have come back to him at the end and he would simply have put it back in the till. Very much like an IOU cancelling out another IOU, but with many people in the chain.
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