Beings like more abstract "not really higher dimensional"
If a character is "truly called" higher "dimensional" or higher dimensions, it means he is extra-axial.(The important thing here is that the "higher dimension" is not used metaphorically or exaggeratedly.)
As the states on the page, writers can use things like "higher dimension or higher plane" in a figurative sense. But if this is used in its true sense, it is HDE.
And one more thing, R>F is not qualitative superiority in the sense of existence. Just being qualitatively superior to the lower plane in terms of power (or being more real).
In short, statements like "higher dimensional" or "higher dimension" usually mean being higher dimensional than lower plane, that is, extra axis, unless used metaphorically or exaggeratedly. Already in the HDE revision, it was said that if it was understood that these were not used in a figurative or exaggerated sense, it would be HDE.