I'm going to give you the conclusion to this article here to solve the tl;dr problem. There are two things the library has done to create such cool projects. First, I'm convinced the NYPL is succeeding online because of desire. The library's employees give a shit about the digital aspects of their institution, and they are supported in that shit giving. I mean this in the most fundamental way possible and as a damning critique for media companies. Second, the library sees its users as collaborators in improving the collections the library already has. While serving them online costs the library some money, they are creating value, too, by opening up conduits into the library for superusers.
Madrigal was obviously pretty smitten to - the Atlantic has put out an open call to librarians, archivists and curators to tell them more about what they're doing:
We here at The Atlantic Technology channel love archival collections that have been digitized. We think they help us situate ourselves in the present by giving us an unvarnished look into the past. We also think that your work doesn't get enough attention from the outside world. Reporting a recent story on the New York Public Library's digitization efforts, we realized that we wanted to create a conduit into our reporting system for you to let us know when you're working on an interesting collection.
So, that's what this form is. A self-service way to quickly ping us about the good work you're doing.