Easter eggs can contain basically anything. In a video game I'd expect an easter egg to be anything from a secret weird level or item, a nod to another game/movie, or a picture of one of the developers' pets. As that bit you quoted from the story was trying to make clear, in the context of Taylor Swift, "easter eggs" are a much more specific and are often hints about what will happen next. This seems like a very reasonable clarification to make, and to my eyes doesn't imply that Swifties invented the term.