That's not quite true. It's a "new engine" if compared to the original 3.3.5, sure.
But it's on the engine they have been using for their current expansions, so it isn't a "completely new engine." It also isn't brand new content, which they are trying for the first time. It also also way more than likely already had a big slice of the work done, as "current" assets already existed for a lot of WotLK areas and content.
So, private servers have been around for 13 years and had different groups working on emulating stuff? True.
Blizzard had not only more time - they've been at it since the conceptualization of Vanilla - but also more people with more resources, mostly working on tweaking existing stuff to recreate an old version, not a new expansion.