In the early days of gaming the story was right at the bottom of the pile for developers, and what story there was tended to be messy cobbled together genre clichés. Luckily as the technology and budgets improved so did the story telling techniques. Games such as ‘Zelda’ began to mimic classic fairy tales with hints of epic fantasy authors. However, many were still very linear with the player simply following a story from beginning, middle and end. Players tend to always be at the centre of the story, the hero. The story of a game often helps us get involved with the experience, its gives us a goal/reason to keep playing beyond just beating your highest score.
This isn't to say every game needs an epic Tolkien-esc plot full of twists and turns. Sometimes you just want to help Barney get his girlfriend back whilst gunning down hapless mutants. Sometimes a games story will in fact be more like a setting for the action to take place. Games like Call of Duty may take place during World War 2, but I think of it more of just a backdrop; a reason to be shooting Germans instead of a 'war story'. Upon thinking about this the same kind of definition could possibly be applied to films. Take ‘Saving Private Ryan’ for example. Is the fact its set during World War 2 necessary for the story? Or is it just a bloody good excuse to film a scene of the Omaha beach landings?