This is not the flexible UAV delivery service you could have imagined. Drones will fly on fixed routes, under the supervision of a trained pilot-in-command. It is part of the FAA's larger pilot program, which tests public-private partnerships involving drones, and involves assistance from the FAA as well as from the North Carolina Transportation Department.
It's a modest start, but it should develop over time. UPS and Matternet both plan to use the Raleigh network to see how drones can be used in other medical facilities in the United States. If all goes well, you can easily see other hospitals using drones regularly.