DDG does have an API for the goodies, but not for the search results because they come from a variety of sources, some of which don't allow sub-licensing.
Seems like you could have a search API for the sources that do allow sub-licensing. But I'm not sure putting search into an API would be a good way for DDG to gain revenue.
What would be the difference between "licensing" the API for private non-commercial use only, and "licensing" the website for private non-commercial use only? I assume the TOS for the website are restrictive to satisfy the licenses they have with others, could you make an API that has equivalent terms?