At a fundamental level, video games are created by programmers, often highly skilled ones. But coders wouldn't have much success without someone to design the levels, write the plot and dialogue, create the graphics, and define the game concepts and mechanics.
These non-programming tasks are what a degree in games and interactive media gives you the skills to do. The same principles can be applied to other kinds of games, such as those played on a board, as well as any media with a two-way flow of information, like many websites.
Some programming courses may be included in the curriculum, but the focus is usually on interface and general design, using software graphics tools, understanding user behavior, storytelling, and so on.
Most people who study games and interactive media, naturally, are big fans of video games. Creative thinking and a proclivity for visual communication are also assets. The opportunities which may become available to you will often not be in your preferred field, so a willingness to become multi-skilled will take you far.