It's absolutely normal not to know. Many universities will have a course designed to help you pick a major, for that very reason.
Meanwhile, don't stress about career paths just yet. Your undergrad degree doesn't determine the rest of your life. Many jobs require a degree, but don't care about the type of degree. For those that do require a specific degree, it's usually a postgraduate degree that several undergraduate degrees can lead into. Science degrees in particular can open doors that you might not have known to consider.
For game design, it's often beneficial to have a wide variety of experience to draw from, though there are programs that teach it. Find something that's fun for you, and go for it.
Personally, I went into college thinking I would enter the Electrical Engineering program, but a few early experiences guided me into an Applied Physics degree. I mostly program now, having decided that while physics classes are fun, the research itself isn't so much.
While studying, find side projects to do. You won't feel like you have much free time, but once you're married with a full-time job, you'll have even less. This is your very best time to see whether you can hit it big with a game design of your own, or to join a small startup. Learning skills through volunteer work can also pay off later.
Most importantly, learn how to be responsible, while still enjoying life.