Wow. I just have to say a big thank you to the Obsidian team for taking the time to answer questions on the forums. I rarely see developers who are willing to take the effort to do so.
There's one thing I should add.
One should not think I want to be a game writer. Instead, your thoughts should be more like I want to be a writer.
Why generalize? There are many different mediums out there, and a diverse skill set allows you to roll and change with the times. In a creative profession - be it - artist or writer, you need to be adaptable. Like Monty stated, write short stories, write plays, write screenplays...everything. Each will allow you to develop your writing skills more than if you just stuck to one medium (at least in the beginning).
The game industry is a hot topic these days. Everyone thinks they want to work in the industry...but do they really understand what it's like? Playing games and creating games are very very different experiences. If you focus solely on being a "game writer" - what happens if you find out that you don't enjoy it?
Enjoy life, and pursue a degree in what stirs your interests. If it is Anthropology or Astrophysics (my first major) ... then go for it!! Don't worry about taking something because you think it will lead to a job - you'll end up miserable. A writer must have a passion for learning...and the more interests, knowledge, and life experiences you can draw on when you write, the better!