I have tested various methods to display videos as live wallpaper and screen savers.
Windows
PTE AV Studio (publish .scr screen saver)
Pot Player (free screensaver)
Wallpaper Engine (wallpaper/screensaver)
Push Video Wallpaper (wallpaper/screensaver)
Lively Wallpaper (free wallpaper/screensaver)
WinXcorners (free emulates Mac hotcorners)
HideDesktopIcons (free download link)
WinXcorners and HideDesktopIcons work well together to start the screensaver or show/hide the desktop icons.
Mac
Dynamic Wallpaper Engine (wallpaper/screensaver)
I know there are other apps but I am happy with this one.
Lively wallpaper can add depth map to bitmap images (like Photoshop neural filter depth blur) so the have slight parallax change during mouse movement.
Thanks,
Tom