They just don't have it. Nothing wrong with that; I certainly wouldn't call it discrimination any more than I would humans not having pointy ear options or dwarves not having horn options. It's a difference. Dwarves balance it out by being apparently particularly inclined to beards in any case, I'd say.
Although personally I do prefer elves not having facial hair, I don't think either way is inherently right or wrong -- that depends on the setting. I would certainly be against changing it in Dragon Age (and in fact would be if they changed it in the Elder Scrolls as well; in both cases the facial hair/no facial hair status of male elves is already established).
If you read literature on elves, you'll notice that 99.9% of them have elves that are incapable of growing any hair other than the hair that is on the top of their head, eyelashes, and eyebrows. Half elves could grow beards though. Take Aragorn from Lord of the Rings. He's a half-elf, and he has glorious facial hair.
Dude, Aragorn's not only not a half-elf (some Elvish blood, yes, but not near half), but there's no proof that he has facial hair and in fact some evidence that he doesn't (as generally if a character has facial hair it is mentioned, and in his case it never is). One of a very long list of things that the movie adaptations didn't do very well at.
I'll agree that half-elves in many other works can obviously grow beards, and they can in Dragon Age as well, if you consider the half-elves of Dragon Age to be half-elves and not basically humans.