One popular hypothesis about the existence of the dream realm is that it doesn't actually exist at all, but is really a hallucination experienced as a result of inhaling the fumes released from burning soaked kindling. This theory is backed up by renowned scholar and librarian of the Library of Varrock Reldo, who discussed what he thought about Dream worlds and other similar planes of existence in Postbag from the Hedge 42. He stated that:
I have heard of many other realms attached to our own but invisible to the uninitiated - lands of fairies, mists, shadows and even a dreamscape where your personal inadequacies are confronted - and I have little doubt that at least some of these are real. I imagine that the majority, however, are allegorical terms to explain some universal human concern, mythologised over the ages to help us understand them in terms we can appreciate.
— Reldo, Varrock Librarian
Although, this hypothesis doesn't necessarily explain why you are able to die a real death in the dream world, or why real-world items can be brought into and out of it as well as be used (such as healing yourself with food that does not reappear due to everything not being real). It is possible that your death in the dream world is a metaphor for something going wrong in the dream process, and it is also possible that you are still able to use real items, even in your hallucinogenic state.