In-game, the shout is referred to as "Unrelenting Force", but it has grown to be known as "Fus Ro Dah" by Skyrim players due to the words composing the dragon shout. Since then it has become something of a joke among players, much like the reference to "fishy sticks", which Bethesda has since paid homage to in Morrowind, Oblivion, and Skyrim. The only difference is that now Zenimax want to own the rights to the dragon shout.
As TechDirt observes, the phrase has gained infamy on the internet due to a variety of videos produced both in-game, and in the real world. Compilations parodying real-world events and incorporating the phrase have grown popular on sites such as YouTube. Some of these videos have reached a million views, and therefore it is probably something Zenimax would like to hold on to. Zenimax are quite aggressive in their pursuits of trademarks: they prevented Markus Persson, better known as "Notch" (one of Minecraft"s developers) from using the name "Scrolls" for another title he had worked on.
The video below is one of the longer compilations, comprising footage from a variety of different sources. The movie buffs among you may notice several films are used during the compilation, alongside other footage.
Zenimaxs reasoning for wanting to possess this meme cannot be determined at the moment. It could simply be as a form of "protection" or control over its usage. The movement could be preventative, intending to avoid it being used in manners they may not have intended (in which case, these videos are probably infringing on that). Should videos be taken down due to a Zenimax lawsuit it is almost guaranteed that fans will backlash against the company.