I haven't heard MRMA before. HEMA (Historical European Martial Arts) is often used, as are the terms historical fencing, historical swordsmanship and historical swordplay. Ultimately as long as it's clear what you're talking about, you can call it what you like.

To get back to the original question about the origins of martial arts, a martial art is a systematic method of fighting that can be taught (I don't see that sporting contests are at all necessary in defining a martial art - some would claim that when sporting contests appear it ceases to be a martial art and becomes a martial sport - nor does a formal school or master student relationship need to be present, if one person is teaching systematic fighting skills to another, then a martial art exists). Therefore martial arts probably originated when caveman Ogg taught his cool moves to caveman Zogg.

Cheers
Stephen