All I know is when my artist was working on this page, she cried, like...a lot.
Essentially, you're just making a big animated gif, but only a little part of the full image moves. So we imported the animation of the portrait, and set up an animated gif in Photoshop using the Timeline window. The newspaper text stays static while the portrait moves. So think in terms of frames: in every frame, the text isn't moving, so it stays still. But each frame has a different portrait image, so when you save it as an animated gif, the portrait is moving.
It's kind of tricky, and the file sizes are masssive, so you have to sacrifice quality. It was fun to mess around with, but also exceedingly tedious, especially when we found a typo the night before we had to post the page.