Since Wallpaper Engine supports .html files, we can set an animated GIF as a wallpaper through this way.
Create a new text file next to your desired .GIF file, call it something like "wallpaper.html".
Open that file in something like Notepad++ (or just Notepad) and paste this below:


Change the "filename.gif" to whatever picture you want as your background.
You can also make it stretch to fullscreen by using this instead:
<img src="filename.gif" width="100%" height="100%">

If the GIF is taller vertically, replace the line I had in the copy-code with this instead.
<img src="filename.gif" width="100%">

You can edit the border color by changing the numbers after the "background-color" area (#RRGGBB, Red Green Blue).
It's easy to find hex color code generators off Google if you're unfamiliar with hex.
background-color: #000000;

Now save the edit in your text editor, go to wallpaper engine and click "Open from File" then click your saved "wallpaper.html" file (or whatever you called it).
Tada! Animated GIF wallpapers!