It was explained to me as Menjin was like a wizard or a superior Master of his art, it had nothing to do with tournament fighting or Champion. At the time that I heard the term this system rarely tournament sparred. There was all types of dojo sparring but they rarely sparred outside the dojo, for a trophy or title.
But I'm not saying that it couldn't have that definition, niether one of us speak Okinawan, just Karate dojo terms.
But it wasn't introduced/defined to me that way.