I've heard it said that role-playing games, especially those of the indie sort, are really about telling stories. I don't think that's the case. We do tell stories, out of game, about the game sessions we've played. All the more reason to play and play well. And there's no question that a character within a game can relate a story to other characters during play. But gaming isn't equivalent to creating a single story or even a set of stories. There's no script - at least, not one that survives much into any given game session. In role-playing games, the characters do interact with and within imagined situations. But it's improvised. The choices and events don't fully merge into some over-arching, cohesive plot, nor should we require that they do so. Any given interaction or event within a session may be enjoyable or satisfying in itself, aesthetically, viscerally, morally. It need not tie into a story arc to be worth playing out.
In that way, RPG's are like life. Though I'm a Christian, I'm not one who believes that everything happens for a reason, as part of One Big Plan. A great many things do happen for a reason, though I tend to be pretty careful about reading meanings into events. God is constantly involved in what we do, but He is under no obligation to make this obvious or to explain any of it to our satisfaction. It isn't One Big Story that binds history together, it's God himself. God involves Himself with His creation in such a way that it can and should be conveyed as story. "Can" because God is intimately involved in events, and events flow from one another. "Should" because we are story-telling creatures. We recognize sequence and closure and, through story, find and create meaning. "In the beginning" isn't just the beginning of all things, but the beginning of a story. And our lives aren't complete without those stories. But a single isolated event can have profound meaning, simply because God is behind it.
So I'm much more open to saying that RPG's are about drama, than about story. Stories will emerge, and our play will be better for it. But there's no need to worry if a party's jaunt through the woods isn't worthy of some novel. It can still be exciting, amusing, or even deeply touching - no script required.