Granted almost any course you do can help you in being a game designer. But I dare ask cause since I'm right now doing an Internship about

Graphic/Web Design, What does that have anything to do with game design?

Graphic design might provide the skills to produce assets for 2d games and to create UI elements, but unless you happen to be developing browser-based games web design doesn't really have anything to do with games at all.

Web design can still be very useful for an indie or hobbyist though if you need to create your own website! ...and of course, any programming practice will help further your programming skills. :)