What is mysticism? Mysticism is the acceptance of allegations without evidence or proof, either apart from or against the evidence of one's senses and one's reason. Mysticism is the claim to some non-sensory, non-rational, non-definable, non-identifiable means of knowledge, such as "instinct," "revelation," or any form of "just knowing." Well then -- suppose you apply this principle to Rand's own premises.
You will find (if you are honest) that her premises meet this definition of mysticism.