Sex & Games

I think that the answer is fairly simple: get good writers!

A good writer that has the ability to create characters that are both believable, in terms of emotional response, and intriguing and that can make all the difference in the world.

For example, I liked the movies Bottle Rocket and The Italian Job, both movies about likeable thieves (simple comparison, but stay with me). In The Italian Job I was basically along for the ride with a bunch of caricatures of people with only a few distinct emotions (anger, love, etc.). The main draw wasn't the characters but the events and I wasn't emotionally invested. Sure I liked the car chases but I could give a crap if someone died because they weren't real.

I actually cared about the characters in Bottle Rocket, because they were "human beings" and showed real emotion (a spectrum rather than just a few discinct). I actually felt with them. The characters were the events (or their actions and feelings dictated the events). When Dignan is in prison at the end, I actually feel bad for him.

In order to evoke the same feelings in games all that is needed is well-written multi-dimensional (in terms of emotion) characters that a player can feel along with. Granted, there also needs to be good direction and good voice acting, when applicable, (I don't see why getting good voice acting is so hard, but I guess it is) to bring the story to life. But because of the interactive nature of video games, the job of sucking a player in emotionally should be that much easier.