Looks like projection mapping. I doubt they crammed it in the base though, are there fancy "decorations" that didn't make the video but are key to the process?
There are a few more pics, video angles, and a YouTube video from Disney Weddings over on the Cake Talk thread. It doesn't really get too much into the how, but you can get some other views of it.
Read on a tech blog of all places that there is an overhead projector that is used to do the mappings. So the cake/table needs to be placed in an exact location for the effect to work.