A recent science study undertaken by University of Windsor professor Casandra Sholy has gone into a good bit of detail on the relationship between video games and the military, along with the increased militarization of games in general and how they affect individuals, military technology, and the military’s economic relationships with the video game market.
The study first brings up (alongside the usual rigamarole about how video games are thought to cause aggressive behavior) the increased use of video games in military training. Video games allow their players to develop problem-solving, reflexes, multitasking, situational awareness, and sharing of knowledge, qualities that the military values.
Players can also learn how to do things in real life through simulators: Lockheed Martin, for instance, is so confident in this that they even acquired Microsoft Flight Simulator and turned it into a game called Prepar3d that they use to train pilots.
Navies all over the world are also making use of video games to train personnel; various older games such as Jane’s Fleet Command and TACOPS are used as simulators and strategy games, and other branches of the military are following suit, replacing far more restrictive and less effective methods of training with video games.
This doesn’t even fully extend to video games; controllers are also used in various instances, such as United States Navy personnel piloting submarines using Xbox controllers, which are far more cost effective, ergonomic, and easier to train. Other things like military robots and more are also controlled in similar fashions.
There is also the most obvious of the influences that the military has in video games: the games themselves. With first-person shooters such as Call of Duty and Halo consistently being some of the most-played games out there, they are valuable propaganda tools that often persuade people to join the military.
All in all, much like war movies in Hollywood, militaries all over the world exert a great deal of influence in gaming, and are seeing video games as a cheaper and more effective way to train their personnel in various fields. You can look over everything in the study in more detail by reading it for yourself in the link above.