Digital worlds in Kingdom Hearts seem to be equally real as anything else, except that they exist on a computer, and the data can thus be edited or corrupted from outside of it. This has been clear since KH2 which showed objects and people able to physically move from one to the other, and that's what all the other games have been working with.
This is a world where dreams explicitly exist in physical reality, so the idea that computer data can be entered like a quantifiable physical existence, more like a pocket dimension, is not strange, although these facts about the KH world are often taken for granted by the characters.
As usual almost all questions about "why does the KH world work in this unintuitive way?" can be answered with "this is a metaphysical setting where stories exist and are alive". A "world" is a metaphysical living story, not a planet floating in "outer space" the way we know it. Ergo a data world is really not that different.