Many "video game design" courses have little to do with game design, instead they are programming courses with a bit of level design or character design thrown in, or they are art, modeling, or animation courses with some design pieces thrown in. Sometimes they are focused on game design from the perspective of a game designer, but they overlook the fact that "game designer" is not an entry level role.
As Hodgman asked, there are many roles available. Saying you want to be the Game Designer is somewhat akin to saying you want to be a CEO.
For an aspiring CEO they might get an MBA degree, but that won't grant them the job at the top. The degree can help give some educational background and training, and will help at job interviews, but that's about it. Similarly a program teaching only the factors of game design won't make you a game designer, but can give you some education background and training to help follow in that direction.
Many people think of Game Designer as the idea guy, the one who comes up with the awesome idea, pitches it, and works with everyone to make the vision a reality. There is a position of game designer and that does some of the things people think of, but it is a management position and a senior development role. The person is directing many tens of millions of dollars of the project, and consequently the position requires years of experience. It is not an entry level job.
There are some entry level jobs working with world design, character design, level design, and similar, but usually they are coupled with programming as script writers for levels, or coupled with art as modeling prototypical worlds. If you start in that track than maybe six or ten years later you can get the Game Designer job title, but be prepared to work for many years on a much less prestigious job description.
All the game designers I know started out in other fields, and demonstrated competence both in game development generally and in their field. As they demonstrated increasing knowledge of design they were slowly given more responsibility for design; helping design small objects, helping build levels, helping balance systems. Over time it expands to owning small object design, owning level design, and gradually after many years transitioning into a designer role.