In literature and film, the most crucial storytelling element is the characters and interaction between them. Compelling characters make up for a lot of slack in plot and setting. Just look at the most popular TV shows -- they're all driven by interesting characters and the hooks involve those characters. Ask a person what they liked about a book, and they'll probably begin by describing a character or a character-defining action. In novels and movies, the audience experiences things sympathetically. We follow someone else's journey and think/feel with that character.
In video games, the most crucial story element is setting. No matter how good the plot may be, the heart of a game always lies with the decisions and skills of the player. The main job of the developers is to create a great setting, and to define how and why the player will interact with that setting.
That's true even in plot-driven games. Plot is undeniably important in the Halo series. But the primary purpose of that plot, effectively, is to make the player feel like a hero and anticipate escalating challenges. There are few exceptions... mostly Bioware games (which I often describe as a blending of mediums -- game and film).
Characters are important in many games, but they are typically used more in line with cinematic goals than gaming ones. They're actors in a script for players to receive, rather than set pieces for players to experiment with and affect.
As Raph Koster has stated many times, play is fundamentally about learning through action. Plot and characters should serve the setting. In a game, the primary value of any character is what the player can do with that character or how that character affects the setting. Plots in a game provide inspiration and change the rules of play (ex: now, you must go this way, use this weapon, etc).
I appreciate games mixed heavily with cinema, like Mass Effect or Ghostbusters, but it's important to recognize such games as a blending of mediums. Games are not about being taken along on grand adventures. Games are about going on the adventures, yourself... your own adventures.