I'm a captain in the Army and have been active for about 13 years now. Personally, I love pinball. Yes, I don't get to play it as much as I like due to those "other priorities," and yes, my paycheck pretty much topped out at one player's condition Firepower. Doesn't mean we/I still don't love it.
As busy as we were in Iraq, one of the greatest things was when the owner of the FLGS (friendly local games store) set out a box where people could dump donations and sent us a huge box of D&D and Pathfinder books, dice, screens, maps... I'm not being sarcastic. It kept people out of their bunks and in public areas, talking and laughing after a bad patrol or another day of nonstop mortars.
My point is that you would be surprised how many geeks and nerds are in the Army. Setting aside those other priorities and letting your mind wander different paths is as important for us as it is for office-hell salary workers.