Almost. Tamarians were using references to shared cultural stories. Many, but not all, memes work like that. This meme is of a different kind - it packs emotional payload mostly directly, with only a reference to a simple activity and related concept (popcorn + Internet drama).

Put another way, if you consider a story to be a collection of handles (in programming sense, like a pointer) to concepts and emotions, then Tamarians communicate by speaking handles to stories. That's one level of indirection extra over this meme, which itself is a (simple) story - a collection of handles to concepts and emotions.