I happen to agree with Bruno Faidutti that a good game is a good piece of writing. A good new game requires enough of a plot to be captivating to new and old players. This is especially the kinds of games I like to play: involved strategy games that expect one to spend hours learning rules and hours playing by them (and, if you're like my friends and me, hours arguing about them).
In the current issue of The Games Journal, Faidutti says:
Like a film or a novel, a game tells a story—but a story which changes with each game. Like a film or a novel, a game is inspired by all the works (books, films, and mostly other games) which have preceded it, and is part of a cultural tradition through references and quotes. This is definitely why I consider role-playing games, undoubtedly the least technical form of gaming but by far the most social and literary, to be the quintessence of gaming. There are of course technical and mechanical aspects in creating a game, testing and adjusting various systems, but the same applies to films and novels, neither of which are considered technical creations.
Children, especially, require a story to hold their attention in a game. Even a classic game like Sorry! takes on an added dimension when, instead of pawn chasing pawn, it's Peter Pan stomping on Captain Hook.
Well, it does in our house, anyway.