The Face with Spiral Eyes emoji was proposed to resolve vendor interoperability. In regards to the 😵 Dizzy Face emoji, part of platforms rendered it with "spiral-eyes", when the other part rendered with "X-eyes".
This emoji can convey a hyperbolic sense of feelings like dizziness, shock, surprise, disbelief, hypnosis, etc. Due to backwards compatibility reasons the Dizzy Face emoji hadn't changed. But the Spiral Eyes emoji helps to distinguish "dead" or "knocked-out" 😵 version from "dizzy" or "hypnotized" 😵💫 spiral version.