Most games don't go much further than that - but I've certainly been made happy, sad, afraid, and thoroughly involved by computer games. They haven't, generally, been as good as movies at doing so, because excitement is so much easier for computer games designers to focus on, and the bits which produce other emotions tend to be quite filmlike or booklike (depending on whether they are produced by reading dialogue or watching a cut-scene).
My definition du jour of "game" is "a process which provides a challenge for a person to overcome". If you're choosing between options which provide multiple equally "good" solutions (i.e. dialogue trees that don't affect your success level), are they really part of the game? So we're left with two parts of computer games - the bits which are challenges to be overcome (which can produce excitement and feelings of achievement), and the bits which are evoking other emotions. If you exclude those two emotions from the range which count as proper art then computer games are a mixture of interactive art and game, without any crossover. If you do include them, then games are definitely art.
If, of course, your definitions of "art" and "games" are different to mine, which they probably will be, as I only made mine up half an hour ago, then your conclusions will be different. There are a bunch of definitions of "game" <A href="http://en.wikipedia.org/wiki/Game#Definitions">here</A> and art <A href="http://en.wikipedia.org/wiki/Art#Definition_of_the_term">here</A>.