Haha. Hi there writer friend! I'm a writer as well, and like you, was interested in joining the game industry as a writer. A little search gave me some useful information to make career as a game writer, and let me tell you some. I was just searching for information, not applying for a position. I'm still young and prefer to work as a programmer.
Write some reputation. Game industry will hardly take you if you don't have any kind of record. There are many indie game projects, and you can start there. If you have some programmer friends who want to make a simple game, offer your service as a writer.
Learn something else. That will increase your value. You may want to learn game design.
Should I be willing to work on writing outside of the actual storyline of the game? for example, writing for the game's website, press releases, instruction manuals, etc.
Yes. Why not?
I also want to know if there are any programs or writing formats I should become more familiar with if I want to write for video games.
I'm not sure about what do you mean by format. Have you ever played traditional RPG? That role play with dice, paper and ink (oh my sweet childhood)? Try to write in the same sheet-like format. As a writer, we're supposed to know every single detail of our characters and we may want to write those details on a piece of paper so we won't forget, even though in fiction writing we don't usually give all of those information to our reader. Here, write everything. Just like while you're role playing. Write every details about characters, objects, magics, monsters, world, places, scenes, or whatever.
Yeah I know that we're not only aiming for RPG, but this format is also needed for any genre. Even FPS games have story lines.
I'm sure that you can handle the story line.