For me I would say that the character's importance in a game varies depending on its genre. But increasingly more and more these days, developers are focusing on developing a story behind the avatar you might play in an attempt to give you that same emotional connection that a good film does with important characters. If you can develop an emotional connection to your Avatar then the world around you and the NPC's that fill it become largely more important and interesting. Dull mindless games ultimately lead to boredom and the novelty of new special effects, increased graphics or new combat mechanics, just doesn't excite in a lasting way for true gamers.
Most films try very hard early on to make you invest in their character(s) so that if something happens to them it will provoke a memorable response be it good or bad. Epic films such as The Lord of The Rings trilogy, directed by Peter Jackson, have a job finding the right actors for the characters that are already alive in the books. And it can be incredibly difficult to successfully give a face to something that has long since existed in the imagination of thousands of Tolkein fans prior. But he pulled it off because he had a vision, like all those other readers and he hunted them down till he found the ones perfect for the job. And it pays off as anyone would know from seeing the films. So i do think that games should consider the appearance of their characters, and sometimes no matter how interesting the story is or the world may seem. If your character runs like he's soiled his pants and was smacked in the face with a frying pan before he learned to talk, well then I think some serious rethinking and redoing is needed. And that is enough to kill any game.
"To create a truly immersive game experience with a compelling fantasy
world, you have to populate that world with real characters. Not just
characters that behave realistically on the screen, but characters that
ARE real to you, the game’s creator. The more you know your own
characters, the more real they will become, and the more they will help
draw the player into your game’s imaginary word. It’s not enough for
your characters to have distinctive speech patterns and tics. They need
actual histories, motives, dreams, and secrets. Then they will have real
depth with which pull the player in, and your fantasy world will be
come a real place that the player loves to visit, and can't wait to get
back to when they leave."
Most games now days that attempt to emphasize the main character you play as and the world your in, have you play in third person view. This allows you to take in more of your surroundings, and to more importantly, view how your character passes through or interacts with the game assets present. Almost like you are the hand of god unseen but every loving and caring for your avatar guiding them through the story. The Mass Effect games one, two I would say for me nearly nailed the character design and story driven 3rd person action/adventure. The worked hard to make sure you had a lot of choice in the game as to what kind of hero or Villan you were going to be as the story lines played out. And it felt quite fresh how they did it with the multi choice menus during dialogues and in game cinematic type cut scene. For most it made you really become aware of the intricacies of the story and think carefully about how you made your decisions as Commander Shepard .
Heavy Rain, created by Quantum Dream for the Playstation three, is a good example of publishers pushing the story telling aspect of the game with a large portion of the game being cinematic in its play style. Meaning you watch your character go through a set choice of scenarios which you influence but they play out without direct control of your character. It was a bold game and quite novel but it did very well and I think since there has been a increase in cinematic games.