Staffers/drones, using Windows snipping tool, cut-n-paste of contents on screen, and forwarding stuff for Hillary with just raw text content and images, stripped of all security headers.
Unless .gov applications, mail systems, and file formats were specifically designed to be proprietary, and defeat at least most of the known common screen capture functions (assuming our .gov was REALLY serious about security, and used non-commercial OS'es... of course not.) like detecting all known Windows API's that can do a screen grab, and a keyboard hook that prevents PrtScrn from keyboard input from dumping the desktop to the clipboard... there's a dozen manual ways a user could defeat it.
Hell, they could have had a staffer sitting at a desk with a smartphone, taking pictures of the screens, and forwarding them to Hillary, and the threat goes out there'll be hell to pay if anyone says word boo about it.