A sufficiently good programmer can have little in the way of artistic ability and still make a game, but it isn't the other way around. However, the reason that artists and programmers are usually separate people is because not all artists are good at programming and vice versa. Designers are also usually different from engineers for much the same reason. With that said, you should be familiar with how a game functions if you want to become a game artist or designer, so you should at least know enough about programming that you can tell the difference between a bogo and a bubble sort.