You wouldn't need to be a computer wizz to be a designer. Not all games have to be computer games, nor be technically complex. Although if you intended to design hardcore digital games, I would assume a knowledge of a computer capabilities, some basic IT skills and experience with industry standard software packages would be desirable.
I don't know about ITT-T but alot of courses where I am have taught us from scratch; working upward from a strong common foundation.
As far as Mac vs PC, etc. From a user perspective, most systems are fundamentally similar. A word processor is still a word processor no matter which system you use. Both are straightforward to learn and use - so I wouldn't worry about it.
Hope this helps!