You could print many frames from a video, and then if you move them fast, you'll have the illusion of a holographic video.

That is very much how the hologram printer works! You take many images, each from a slightly different perspective (maybe every 1 degree), and the hologram synthesizes them into the full 3D image.

The other cool part is the holograms can have motion as a result.

So as you move the hologram back and forth is will move!