This entire train of discussion makes me feel kind of weird about having A. Never read the Sandman comics but also B. Feeling like I pretty well 'got' what was going on in the story.
It's mythopoetic as hell, but sure, but it's not just Gaiman. Gaiman was, to at least some degree, drawing on the well of 'real' mythology concerning the nature of reality and the idea of consciousness defining the world rather than the world defining consciousness. Spiritualism vs. Materialism, in Stellaris Empire terms.
Like, the story is a specific reference to Gaiman's story, sure, particularly the details with the cats, but that's not the important bit, narratively speaking? In the context of a character who quite literally shapes reality according to his desires.
I think the most confusing thing here might be how it's written as a dialog, but we're only directly seeing one side of the conversation. We're left to infer what the speaker is responding to, based on what is being said. Another character is implied to be present and interacting, but we don't see or hear them at all. They're not shown, so it's like we're hearing one end of a telephone call rather than watching two people talk, which can be a little disorienting.