You can use that skill, in fact it's necessary. My fully athletically skilled sim loses her fights against them so I think being a skilled martial artist is a necessity to beat them. They just don't use martial arts when they fight them, which I think comes down to laziness in development.

Yeah, I've always hated how they use the regular "Fight" animations. But the martial arts skill is supposed to increase your chances of winning the battle--which is why I brought up AwesomeMod previously, since it fixes the skills to actually work.

I think the reason the developers chose the lazy route was because they didn't want to animate fights where one sim knows martial arts and their opponent doesn't.