I understood it when I was 4...
I could say from similar experience, since I got it when I was 7, that I understood it as well, but not to a total degree. The combat I got, the general quests I got, but sometimes I'd do an action and get dark side points for it, and I couldn't understand why. Now I was considered mature for my age as well, but it wasn't until I was around 10-12 that I truly got the full experience, meaning I understood how to properly complete quests so I could get whatever light/dark side points I wanted.
I don't think it's possible for someone who is still a child to understand how society works, how people in real life work, how they handle conflict, etc. At 4 to be playing video games that require nothing but gameplay like COD, Halo, etc. is perfectly reasonable. For someone to understand the social context, dialogue and complex plots of a video game takes a higher level of intelligence, and that isn't something we develop until we get to elementary school. At ages 4, kids are learning to draw squares and know about 1500 words. I don't think that qualifies as being able to understand the complex plot, the understated aspects and the way society works for an RPG.