While you are correct that "tanuki" is the Japanese word for the Japanese "raccoon dog" (Nyctereutes procyonoides viverrinus) there is also the Japanese badger (Meles anakuma), just to add to the confusion!
In P. Craig Russell's graphic novel version of the same story, he actually illustrates the animal in question as a badger (which it is called in that version of the text) - see: http://page247.wordpress.com/2010/04/19/sandmanthe-dream-hunters-by-neil-gaiman-and-p-craig-russell/