Now, I can imagine your surprise when seeing the game I choose is Battlefield 4 since it's an multiplayer shooting game but believe me after playing this game for half a year I have known so much about military technologies that it shocked me how much efforts we humans have put into this sector of technology (the technology for killing each other).

What Battlefield would teach it's students:

 This game can help students learn the below:

Why would Battlefield be a good educational game:

There are a lot of people ignorant about military technologies and by having a basic idea about it,  will help you understand politics better, so that the next time you hear in the news that the Syrian government has added reactive armor technology to their vehicles you would understand what that means.

 Reactive Armor

 http://www.elec-intro.com/cms/plus/view.php?aid=8937

 You have probably seen these small boxes on tanks before in the news and you may have thought that they are made of iron or some kind of metal to protect the tank. What if I told you they are actually high explosives! You would think why would someone put bombs on his tank? 

How Battlefield would teach:

While playing Battlefield, each time you upgrade your vehicle with; sabot shell, TOW missiles, thermal optics, thermal camouflage, armor piercing projectiles, reactive armor, active protection countermeasures, etc, you would want to know how to use it to defeat other players and then at the heat of competition you will slowly find yourself doing small researches about them.

   A Sabot Shell is a tank round consisting of a high density, dart-like kinetic energy penetrator (KEP), propellant, and a sabot (shoe) 

 Now, when I was playing battlefield and I want to hit a long ranged target while driving the M1 Abrams tank, then I wouldn’t use the HE shells since they are heavy and they won't reach far, a better idea is to use the Sabot shells since they have a longer range. Did I know this before playing battlefield? Nope, but battlefield taught me.

     http://www.mod.go.jp/e/jdf/no19/news.html

  Have you ever seen a video where a tank is releasing a smoke screen? Have you wondered why? In Battlefield I faced this problem where I find myself being “painted” with laser (laser painting is when a laser guided missile is locking on a vehicle) and there was nothing I could do but being hit with the missile (Lator on I started to use Active protection), so, after doing a research on it in the internet, I discovered that smoke can actually scatter the laser beams and so I immediately tested it out in Battlefield by releasing a smoke screen while being locked on by a laser guided missle and it worked, the missiles were unable to lock on me anymore, as long as there were smoke around me.

 Battlefield won't only teach you the technology, but also real military tactics. Try to search for “battlefield 4 military tactics” you will see many videos and articles about it.

Conclusion: 

 I believe Battlefield can teach soldiers and common people military technologies and military tactics in a way full of fun and competition.   

References:

* http://books.sipri.org/files/FS/SIPRIFS1604.pdf