Before I tell you a little story and my advice just know that I personally prefer to work on my own or with a small team and my goals are for independent game development. If yours are different then adjust my advice to your own personal situation.
I took a Digital Media and IT course twice, first two years I did web design / 3D modeling and animation and the second run of it was mostly programming (C#, XNA, Unity3D) / math classes and a game design class, a total of 4 years. Now this is more of a personal opinion about going through school to get your game dev experience, but depending on your institution it's usually not that great to go for game development specifically. I believe that the main reason you should go for these kinds of courses is if you want connections. Yes, you do get some book knowledge experience in these fields but unless your school is really focused on it you may not find the path you're looking for, or feel confident going into the industry when you complete these courses.
My advice to you would be to figure out which side of game development you can learn on your own. Go to youtube or search on google for free online courses, tutorials, or articles about the subjects you are interested in. Try to see if that kind of workflow and teaching method is easy to follow and when you feel confident with that learning process the opposite is where you should continue your education. Let me give you an example. A couple months before I started my third year ( second run at my Digital Media courses ) I was learning on my own how to program in C#. It was in the form of online video "courses" and I basically went through the basic usage and understanding of the C# language. At the time I found it very challenging but looking back at it now I realized it was actually much easier. By the time my classes started I was already starting to create basic games in XNA and the first couple of classes were a breeze ( also took them four times as long to teach me the same content I learned on my own).
So now you have to ask yourself three questions. One, which is easier to learn on your own. Two, which of the two are you willing to focus the majority of your time on OUTSIDE of class and for the foreseeable future. Three, do you plan to work by yourself or with a small team that you find ( independent ), or do you want to be hired by/apply to a company for work. And as you and others have said, make as many games as you can as fast as you can and finish them, if you choose art then CONCEPT games - it still counts. It's not easy to do a lot of the time especially if you work by yourself but it'll give you the best kind of experience that no school or "tech demo" like project will.
I hope that helps you decide, GOOD LUCK! :D