What aspect of "game design" are you looking to enter? Graphics engine? AI? Portability? etc?
I'd imagine that if you're after the graphics side, you'd need a laptop with a top-end graphics card (ARE their laptop models with Quaddro/FireGL cards out there?) On the other end, backend programming would require a beefier processor than normal.
Probably the best thing for you to do is look at the specs of the laptops the school offers and try to find a deal with the same spec or higher. I mean, the school is going to know what's the best setup for their program... Or, as one of your profs.
--JamesT