This game is known in Japan as "Taisen Karate Dou - Seishun Bishoujo Hen
This [Player vs Player] version was released in October 1984 (one month after the original version). However, it differs slightly from its single-player sibling. There is a greater variation in backgrounds, for example, with a variety of outdoor locations as opposed to the standard martial arts dojos of the earlier version. The sound effects also seem to be a little 'sharper', with the speech, in particular, much improved.
This version of the game can be seen in the 1988 film "Bloodsport".