Perhaps, but did you notice that one of the puzzles actually involves scraping through ITA's own database to find round-trip flights to Chicago? That seemed like a good touch, asking the interviewee to replicate a small part of ITA's own functionality so they could understand the magnitude of the problem.
Actually it sounds like a pretty easy problem from this far out, but maybe if I actually worked on it I'd discover it was trickier than I thought.
Sounds cool, I'd gladly do something like that if they were paying me. I think a good solution is to define a well-scoped project and bring candidates on board on a contract basis to implement them. This contract basis project can even be done remotely. This offers the candidate a chance to learn about you, you can learn about the candidate, and in the end you can both decide what is best for you.
Actually it sounds like a pretty easy problem from this far out, but maybe if I actually worked on it I'd discover it was trickier than I thought.