I would agree that members of the military do have a tough and - in most people's case - frightening job, especially when they are overseas. However, shouldn't the message of the Gospels be enough? What makes a "military" Bible so different from other Bibles? Do they change the words? The only thing I have ever been able to notice is that they will usually include a handful of pages (if that many) of pro-military stuff and then they are usually either covered in a flag pattern or occasionally in camo. I could see how maybe you would have a military study Bible, with many articles and footnotes that relate to the military. However, any instance I've ever seen of a military Bible just glorifies the military in a handful of pages with some quotes taken out of context from the rest of the book of the Bible, and wrapped in a flag and patriotism. All the ones I've seen in stores seem to just glorify the military, the state, and war. I don't see this as productive to anyone's soul's state.
P.S. I have no idea what they were saying in the video, and so my question could be totally stupid, but couldn't those Bibles in the video simply have been camo on the cover so that they could blend in in the event they are present at a battlefield?