Splitting up large pieces of artwork will not help at all - in fact it could end up using more memory and causing problems with seams.
The blog post is advising to use the same technique as Rayman Origins. Despite being a beautiful game, it does not use any large pre-rendered images like you have: it's entirely built out of smaller images. That is a far better way to design games. With the single large piece of artwork in your post, there is nothing you can do, it is simply going to use lots of memory, and you can't reuse it anywhere, so the temptation will be to continue using more and more large images until you completely run out of memory. A game like Rayman Origins on the other hand can keep going with huge levels reusing the same images without using more memory.