When you watch a show like Red vs. Blue, you have to sometimes ask yourself what on earth the writers were thinking when they made this. Who sat there playing Halo and said, damn, I can really see these characters as some misfit soldiers living their lives in this game? In a way, some games build up these possibilities within themselves, to the point that imagining a story for your own character is a game within itself.
What exactly do I mean about this? For example, the other night I sat with SoulCalibur 6 on my TV screen, scrolling through countless clothing options for my custom character. I got to the point where I copied and pasted the same character over and over, creating multiple different costumes for what I imagined were different stages of my own characters life. From soldier, to rogue, I made up my own story for my characters past, imagining organizations and evil characters and all kinds of other things that don't even make sense to the original game. This is similar to Red vs. Blue, in which a whole story was built of assets provided by a game.
It's interesting how some games almost seem to encourage the player to develop this "headcanon" for your own character, even if its not necessarily true or applicable to the game's own world. I'm not sure if this is always intentional or not, because many games that allow the player to customize themselves already have an in depth lore developed by the story mode. It's interesting too, because this can both add and detract from games. When the player's background is left open ended, it can be really fun for the player to let their imagination run wild. But at the same time, sometimes having a well thought out background provided by the game can lead to more satisfying character development later.
So when I end up watching Red vs. Blue, I not only think about the writers, but also the game developers. When a game is made, I imagine they have no idea how the players will react to it. Ideally their goal should be for the player to have fun by any means possible, but some take it further, and the game becomes something more.