[informatimago]

If the interview project is obviously an exercise, and not something that will go into production for this enterprise, then it is fair game. They could have been a little more honest upfront telling you that the opportunity was closing for lack of budget, but nobody lost in the interaction, not even you: you got to perform an good programming exercise, and increased your own professional worth (granted only a small increase assumedly, but still). Or even, you could have fun doing it and that would be enough.

On the other hand, if you developped a feature that is not present in their product, that would fit (then you've got your hint), and if you see this feature appear in a couple of weeks or a few months in their product, then one would find indeed that you'd be justified to invoice them for the work done. Even if they made it do by hundreds of applicants and only selected the best one, it would still qualify as well as work, and they would have to pay everybody IMO. IANAL, so you know what to do.