I'm not a practitioner of the martial arts - at least, not the Oriental variety commonly associated with the label - and really don't understand the mysticism that goes along with it. I do, however, know that to shoot well, one must clear one's mind of other concerns and concentrate on the task at hand, whether it be hitting a bullseye 50 feet away or figuring out how to get through an IPSC course the most efficient way and then doing it.
In the process, I've found that one achieves a certain state of focused calm that's quite relaxing. Blowing off a box at the pistol range used to be one way I'd take care of stress (and isn't now only because I haven't found a place to shoot near Fairmont yet). It's been pointed out that that's the same kind of thing that martial artists seek when fighting. Sounds plausible to me.
If so, that explains the attraction, as geeks like that kind of state. All I know is that I haven't been shooting enough recently.