To understand why jrpgs are role playing games, you do not analyze the words "role playing game." There are plenty of words and phrases in languages for which trying to break down the parts doesn't allow you to arrive at their true definition. The real definition comes from how words are used.
The simple answer is, jrpgs are rpgs because over a long period of time, people have consistently said they were. The Final Fantasy series, for example, has been pointed to as a clear and accepted example of a role playing game franchise. It's fair to say that the absolute definition of "rpg" has changed over time as the term has been accepted in reference to many games and the commonalities between those games which seem to distinguish the genre have been accepted as being definitive. It has as such come to be that those traits themselves define the genre even more than the phrase "role playing game" itself. Obviously "playing a role" is one aspect that's common to rpgs, but it isn't the only one, and to satisfy most people's definition of a role playing game, you generally have to match more than that.
