Anyone that has a website can sign up to be an official Best Buy affiliate; similar to Amazon's affiliate program, if they get approved, they get a small percentage of all sales made through their site.
This approach has paid off for Amazon, which has the dominant affiliate/API program; you can find many examples of what can be done with it in our list of 40 Amazon-related tools. With Remix, Best Buy hopes to become the Amazon of electronic goods. To make sure they're doing it right, Best Buy has employed Mashery, a company whose clients include LinkedIn, Compete, MTV and Netflix, to manage the API.
It's not just a matter of launching the API; developers need to be motivated to create applications for the platform. Best Buy plans to promote it at this year's SXSW Interactive conference; and, of course, there will be competitions and prizes for developers there.