Hi. Game writer here.
to you both.
Game scripts aren't always or often public because they can be messy and the format tends to depend heavily on the game in question and its implementation/pipeline. I wouldn't write a big long Word doc for a heavily branching game because it's hard to follow and harder for other team members to read. Sometimes game dialogue (think barks) is written in Excel, or in proprietary dialogue engines. (It's also often written in Twine format and if you're interested in getting into writing for games this is a good format to learn as it comes up a lot in samples.)
Cutscenes would usually be in screenplay format but not every game uses cutscenes extensively. Similarly, a AAA game script is going to look different than an indie game script because they're developed in very different ways. Example: in a AAA script, I'm more likely to have to write extensive stage directions on a scene to guide a cutscene director on the animation team (which is often in a different studio). On an indie team, I turn around and call across the room/Skype to the animator, we work out what we can do on a whiteboard, and I adjust the script accordingly.
A lot of games writing is done freelance but some of the larger studios do have narrative teams, encompassing narrative designers and writers. The narrative design is just as if not more important than the actual text, because games are always interactive.
The single best way to get into games is to make games. If your high school course has any opportunity to make something, even something small, grab it and run with it. Start building a portfolio now. Some of the early stuff will be crap, probably, but the important thing is to learn.
If you're particularly interested in writing, look at writing courses in university, as well as English. I did a journalism/English combined degree. It's helped. Learn to write overall. Then learn to write for games.
Keep diving into the broader parts of game design and other disciplines as well (animation, engineering, art, sound). Very few games start with story ideas and coming up with them is not an entry-level position. The more hats you can can wear, the more valuable you can be to a small team where you can take charge of what story a game has. Learn to scope. Learn to work with player agency and how play systems work. Watch
Extra Credits on Wednesdays--they're great for looking at how games work and the episodes are written by game writer James Portnow.
Write everyday. Experiment. See what happens. No word is wasted.
Also, games writing does not pay particularly well. Games roles in general don't--a programmer can make more in corporate than in the games world, though like anything it's not bad at the higher levels. There is a lot of turnover in the games industry as studios flourish and then close. If you're interested in this kind of thing, Gamasutra publishes a semi-annual salary survey,
though the most recent I can find is for 2014.
