Does a med spa in Rhode Island need a medical director?

Short answer
The cited rules do not settle this — none of them require a "medical director" title. They establish only that diagnosing, treating, or prescribing is the practice of medicine, and that practicing it without a license is a crime carrying fine or prison.

Rhode Island’s practice-of-medicine definition reaches holding out as well as doing: a person is regarded as practicing medicine who holds themself out as able to diagnose, treat, operate or prescribe for anyone ill or alleged to be ill, or who professes to heal or undertakes by any means or method to do those things — and attaching M.D., D.O. or a similar abbreviation indicating engagement in treatment or diagnosis is itself practicing medicine. The delegation ground is stated as unprofessional conduct: practicing medicine with an unlicensed physician, except in an accredited preceptorship or residency training program, or aiding or abetting unlicensed persons in the practice of medicine. On the cosmetology side, esthetics is defined as cleansing, stimulating, manipulating and beautifying skin, including the treatment of skin problems such as dehydration, temporary capillary dilation, excessive oiliness and clogged pores.