Can video games instill in me a sense of catharsis? Why, yes, and for many reasons, at that. It can be because a video game is brilliantly designed (aesthetically or otherwise), with a rich and layered story that ties into virtually every facet of the gameplay and forces the player to question his very nature as a game actor and human being, or it may as simple as a single scene. A few times I have played games I did not want to finish - I have never experienced this when reading a book or watching a movie.
In fact, movies, on average, are no better off than games, as I rarely feel anything during 'heartfelt', cinematic moments - and that goes double for the Spielberg school of gauche sentimentalism - and literature tends to affect me on an intellectual, rather than emotional level.
Reasonable touched upon what I consider to be one of the chief exigencies of modern video game art. The elicitation of emotion (and, indeed, any kind of narrative) through gameplay experiences is, I think, one of the most powerful storytelling techniques available in any medium. It is, sadly, not seen to a large extent in a majority of today's titles.