You can’t, Facebook isn’t supporting animated GIF images and once posted it’ll be flatten.
What you see in the sample you’ve provided isn’t wall but application running in Page Tab, those applications are not part of Facebook and developers are free to do whatever they want unless it not violate platform policies…
Update:
Aside of link you provided in question the one you refer in comments indeed profile with animated GIF images in feed stories. This is looks like a bug (probably discovered in the last couple of weeks, I didn’t able to find anything like this dated earlier, and I hope it’ll be fixed soon. In fact there already was a bug with animated images a wile ago that should be already fixed).
BTW, I filed a bug and waiting to get some response from officials on the subject so things may be clarified…
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solved GIF pictures on Facebook wall [closed]