The Game is an abstract concept. It involves no tangible objects, nor is it played on any physical medium. It exists in the minds of those who play it, and it never ends. That's right, you can never win The Game (though this is debatable).
In order to lose the game, you have to think about the game. Upon thinking about the game, you lose and must announce that you've lost. This forces others to lose the game, and spreads the game to new people.
So, you are now playing the game. You will soon forget about this definition, and maybe sometime soon be reminded of it somehow, thereby losing the game.
Mike: Do you want to play a game?
Kieran: Awww man! I lost the game!
Mike: Dammit, I lost the game too.
This term is another way to use the phrase "That's what she said." in normal convorsation. In most cases, people are made to guess what 10-5 means by listening to other people use it in context because the people using it have serious issues.
Mike: We have to go!
Sean: I'm coming.