Hey Kio
I'm not into game design but I'm getting my degree in media and computer science. What I can tell you from experience:
There are a lot of different aspects to game development. Storytelling, programming, visual design, project management... those are only a few.
A lot of those things you can get into by yourself.
Download blender and play around with it. It's free and there are a lot of tutorials online.
Start learning a programming language (I'm not an expert, but I think C/C++ would be a good start, maybe play around with openGL).
Go to a large book store and get a book that catches your eye (maybe game programming for iOS, introduction to Maya, physic engine programming, whatever, doesn't really matter, what you need is a starting point) and work it through.
I always enjoy looking through magazines like PAGE for inspiration.
If you get into it and still think it might be something you want to pursue in the future, then there are many options.
ZHdK has a game design program.
SAE has similar programs and you don't need a matura to enroll.
You might also want to look into less specific programs since they might leave you with more options if you decide that the game industry is not for you after all. FHNW has the iCompetence program which seems quite interesting. And there are always the computer science programs at almost every university. At the universities, you can usually choose from a lot of different modules, including multimedia / computer graphic classes.
Get started and post the results!