I think games are fully capable of it. It is only a matter that people only want specific types of games which makes such games hard to make and appeal to people. For example, I fully think Silent Hill 2 takes advantage of the gaming medium fully - at least by merit of interactivity and not gameplay, while at the same time telling a very personal, thematic, emotional story. It isn't a matter of whether games don't have the ability - they do - it is matter of whether gamers want this type of experience or not.
And considering most gamers have the attention span of an ant, we can conclude that they don't.