I believe that the stage moves the way RainbowCruise does in Melee. There are a few good reasons I think that it is this case. One is that there is no platform that brings you around that stage. In one picture on the roof of the castle the stage is differently designed than in the inside of the castle. If you are saying that the stage is moving around like Delfino Plaza then that would mean that there was a platform that would take you around everywhere.
Also, in this picture
http://www.smashbros.com/en_us/items/assist/images/assist01/assist01_070702e-l.jpg
we can see a draw bridge. Mario is close enough to this draw bridge that I would think it is able to be walked on. In the left part of the picture we can see what appears to be part of the roof of the stage but it is hard to tell because of the nintendog in the way.
Obviously, your first thought of the drawbridge would be that it would lead to the interior of the castle. So thus this leaves me with the conclusion that the stage moves around like it does with RainbowCruise. Although I think the difference between the two stages may be that instead of constantly moving the level around the castle stage stops once it gets to a significant spot and continues after a certain time period has passed. Although this is all theory and it could be something totally different from what I believe it is.