EA Sports thinks that the Commander-in-Chief's Trophy is awarded to the winner of the Army-Air Force game. They even wrote up some crap about it, thinking that Army actually won it in 2006 from Air Force.
It goes to the winner of the games between the three service academies. Yes, the Army-Navy game can decide who wins the trophy.
Anyone with an ounce of college football history could explain this. Unfortunately, no one like that works at EA Sports.