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Martial arts here (2.5 years so far and enjoying it), and I am a military brat myself. My dad, a wargamer and also into D&D was the one who got me into gaming and was also a black belt (or its equivalent) in a few martial arts as well.
Take for that what you will.
As for why, I think being in the military or martial arts takes an amount of focus and dedication that leans itself towards gaming. Also, for both, it's a nice respite away from serious work (either the military duty or the exercises that go with martial arts).
My opionon on that anyway.
I don't know for certain if I took up martial arts because of my love for the parkour-like grace with which classical ninjas and assassins alike dance across the cities of many an old action flick and defeat a hundred men with nothing but a butter knife and a piece of twine, or if I came to like that pop culture stereotype so much because it resembled the martial arts I already practiced, but either way, there's a definite connection.
I am a black belt in Tae Kwon Do (with an emphasis on its origins in Subak, an ancient guerrilla warfare art consisting almost entirely of joint locks and throws), and Krav Maga (a street fighting art developed in Israel which focuses on decisive, merciless strikes to vital areas in order to violently neutralize your target as quickly as possible), and I have practiced (in a much smaller quantity) both Kenpo Karate and Ninpo or Ninjitsu.
My characters in RPGs almost always show this. If the system has a Ninja, I play it. If it doesn't have one, I tend to cobble something together that's similar, generally involving a particularly stealthy and brutal Monk of some sort.
It's probably just me, but I have a hard time believing that a sub-culture that has inspired the memes "gamer time", "fat beard" and "gamer funk" are also primarily part of two life styles known for their self-discpline and structure.
Or in other words, I think most gamers on the internet say they have had a background in it, but in real life probably have not.
On the whole though, I don't necessarily think the percentages average any way or the other. I know plenty of wargamers who were in the military, none of the RPGer's I know were, and there's a sprinkling of martial arts in there. No more or less than those who play Basketball, Baseball or just don't do anything.