The computer science techies can tell you about the technical / programming side of things, but keep in mind that by the time you graduate from university the technical terrain might look rather different - since things change so rapidly and even industry insiders don't really know where the tech is going.
But what about finding a space to learn about how to meld story, characters and setting? Find out which of your favourite PC games come with good level editors / construction kits, and join the modding communities around these. If you can make awesome new free levels or mods for your games, and then tell university admissions officers "my levels / mods had more than 500,000 downloads!", that _might_ give you an edge over others when it comes to getting a place on a highly competitive degree course or internship. They will favour the people who _do it_ and know it, rather than those who just know it in theory and exam-room learning. People who can open up a portfolio of their amateur work and say: "that's a screenshot of the coolest game mod of 2012 - and I made it".
I know _Elder Scrolls: Skyrim_ is out in November, quite possibly the biggest PC game of the year, and like previous Elder Scrolls games it comes with a fully-fledged free Construction Kit addon package for modding anything you want in the game. You might join the _Elder Scrolls: Oblivion_ modding community now, and start learning the basics and the existing Construction Kit, in anticipation of being part of the immense outpouring of fan-generated mod content that'll be happening for the game over Christmas 2011.
The same advice goes for animations and websites. Just download software (Muvizu is free for 3D animations, and SiteGrinder lets you use Photoshop for complete web design) and start making stuff. Then get a free WordPress.com blog and tell people about it and show them pictures of what you're making.