Yes. And that game is named Dreamfall. When video games reach a point where the interaction with the characters becomes so profound that their triumphs are our triumphs; their failures are our failures; we live through their sublime moments, weep with them when they are hurt, and feel loss when they are gone.

All media that communicate can tell a story. Video-games are no different than books, comics, movies, or the voice of a storyteller in this respect.