Digital storytelling is just the most recent upgrade so to speak. Digital Stories are stories in a digital medium. There will be various characters with flaws, there will be obstacles which must be overcome, there will be a beginning, middle, and end. As with all good art nothing will be in the story which doesn't serve the purpose of moving the story along to reveal the mystery and meaning of the story. Unlike traditional storytelling digital stories will be told with graphics, animation, sound and text.
Digital stories start with a sketch in either text or images or maybe both, the story board.
Computer games are very similar to digital stories but computer games diverge away from pure storytelling because computer games are interactive, non-linear. Good computer games have multiple possible endings. This is true human-media interaction. People don't want to interact with hardware or software anymore than they want to interact with paper, they want to interact with the representation on the page and the screen, with the message in the medium. If you sit in the front row of your neighborhood multiplex and watch Jurassic Park you cringe when the Raptors appear.