The Realm of Fantasy is stated to be the dream within the dream, and a realm beneath the Realm of Dreams. For the latter statement, taking into account the former statement, and the fact that dreams, with the right context can be used for R/F stuff, shows that it's not an indication of it's position in the cosmology, but rather the Realm of Fantasy's dimensional inferiority to the Realm of Dreams. So in the context of dreams within dreams, it is talking about layers of reality, and not something like immersion.
In other words, this tells us that the Realm of Fantasy is a realm embedded within the Realm of Dreams, is a lower plane of existence, and there is a R/F difference, which checks the boxes for lower/higher dimensions. Of course, this same relationship exists for the Realm of Fantasy and Kiran's Dream, where the former is just a dream to the latter, making the latter Tier 1.