As I understand it: Project creators log in to Kickstarter and utilize a Chrome bookmarklet provided by BackerKit, which then reads/scrapes the backer infomation from Kickstarter and sends it to BackerKit.[1]
It's kind of messy, but frankly ingenious considering there's no alternatives.
One of BackerKit's founders is/was involved with Diaspora, which was a Kickstarter project. Having the Kickstarter project admin interface (with actual backers) handy to develop and test the bookmarklet against was probably quite a boon. I could be wrong, though.
tl;dr Kickstarter really needs an API.