Even if a soldier was somewhere with relatively stable internet, they likely wouldn't be allowed to go onto XBO Live anyway (or the equivalent with the PS and Wii): hell, PC internet is heavily restricted to begin with (any kind of gaming sites, even if just a forum talking about a game, are likely to be blocked). Let's face it, soldiers like to talk. And while we are constantely told to watch what we say when off duty, chances of sensitive intel being overheard by those that don't need to know it is still there.

In my experience during my own time overseas when still military, none of our gaming platforms (aside from the PC) were allowed to be connected to the internet anyway AFAIR. Offline only, or LAN with other soldiers on base, that's it. All due to security reasons. Requiring a console to be online, with a device that transmits both video and audio (Kinect)? Yeah, that won't fly with OPSEC. From what I've heard, the military (worldwide) have already decided to effectively ban the XBone on their installations for that reason and MS's statement of 'deal with it' to the military does not help their image at all (I'll try to find a source for that, I heard it second/third hand).