Let's make it easy and say everything in our universe is "normal" and the mirror ones are prime. The Enterprise is in our universe and the Enterprise Prime is in the mirror one.
It's a nod and wink to viewers and a little extra effort to say, "It's a mirror universe, it's backward."
Mike Okuda was Scenic Art Supervisor for Enterprise and in charge of the remastering of the FX for the original Star Trek. (For reference, he and Rick Sternbach wrote the technical guides for the newer shows and the actual writers' tech guides, so he not only knows Trek canon, his job for over two decades was to define it.) He was responsible for much of the look of Trek for his time working on the different shows.
With this level of expertise working on the show, it makes it almost impossible to have a mistake like having the Earth rotate in the wrong direction. In addition, any FX studio that does space shots will have a stock set of commonly used models, and Earth would be one of those. It's as much their job to know how Earth rotates as it is for a Doctor to know how to use a stethoscope. So if it's rotating backwards, someone, somewhere along the line, would have to specify that. It is not an accident.
As for it being intended to say that Earth Prime rotates backwards, we can check that by looking at footage from the mirror universe that was created before and after that episode to see what the "rule" for planet rotation in the mirror universe was before and after this episode was made.
In the sequence in the original Star Trek episode Mirror, Mirror, during the sequence when the landing party beams from one universe to the other, the Enterprise orbits left to right and the Enterprise Prime orbits right to left. However, bot the Halkan Homeworld and the Halkan Homeworld Prime orbit in the same direction.
We can check after that episode by looking at the remastered version of Mirror, Mirror. In the remastered version, we see the same change in direction for the Enterprise and the Enterprise Prime. There is no change in direction between the rotation of the Halkan Homeworld and the Halkan Homeworld Prime.
It's worth noting, though, that in the original version, both planets rotated right to left and in the remastered version, they both rotate left to right. Perhaps this is a bit of a nod, as well, to the symmetry of the universes.
This shows they not only intended to keep the different orbital direction matched, but that they could have changed the rotation if they wanted, from one universe to the other but they did not!
It also shows the rule for planetary rotation is the same for both universes.