While DDG uses a myriad of data sources, it's main search functionality is powered by Yahoo BOSS API. They should easily be able to switch over to BING API as Yahoo BOSS has delivered 100% Bing results anyway. However, the ads that DDG shows, and therefore their whole business model, are also powered by Yahoo BOSS API. So they will be able to continue their search engine but they won't make any money from it unless they cut a new deal for search ads.
What's also interesting: Yahoo didn't really anounce this. I'm a Yahoo BOSS customer as well and I haven't been contacted by anyone. I only found out by randomly visiting their website.
They emailed everyone. I submitted this a while ago:
Thanks for the link, I haven't seen this. I just checked again, they didn't email me ..
Actually it powers a lot of search engines. At Blekko we used it to fetch the "long tail" for searches where our index came up short, but we also tried that with Yandex's english index (they had invested in us and they had a similarly sized index).