There's a thought out there that all games have a story, because even in a game without an authored plot, you're constructing a narrative in your head of what's going on. This is what is the most important part, say its adherents; the experience you come away with is the story.
This has never sat well with me. To my mind, this is nothing but a semantic argument intended to obfuscate a real and meaningful difference between games that do, and do not, have an authored narrative. I maintain this is an important distinction, and trying to erase it on vague philosophic grounds does us all an enormous disservice.
But I've been hard-pressed to explain why. On the face of it, these semantic arguments aren't wrong, not exactly. And yet agreeing with the idea that you still get a story even out of a game without a plot misses an important point.
Inspiration has struck! So here I have an extended analogy to explain why I find that way of thinking so insufferable, so dismissive of authored narrative, and why there is a qualitative difference between the two kinds of experiences.
A game with an actual story in it, like Mass Effect, is like a restaurant. A game without, like Minecraft, is a grocery store. They both have the same net result: You get a meal (or an experience). But the process by which that meal arrives is so markedly different that you simply can't elide the two experiences under the banner of 'eating' and expect everything you say about the one to hold true of the other.
Look at how this analogy plays out: In a restaurant, you get fewer choices about the meal you're going to have (but not none!) In return, you can expect the chef to provide you with a certain baseline quality of cuisine -- a story with good pacing, characters, internal consistency. In a grocery store, the choice you have is vastly larger, but you're also going to have to put a lot more work into the experience to come away with an actual meal -- or a story that compares to what a chef might prepare.
As with games, sometimes the home-cooked meals will be the most meaningful to you; the holiday dinners with your grandmother, for example. But few of us are professional chefs, and so if we're looking for a sublime and surprising culinary experience, heading to the grocery store is not our best bet.
But there are also hybrids; buffet-style restaurants, if you will. These are games like Skyrim; series of authored pieces, where it's up to you to determine whether and how to fit them together into a proper meal. Not quite an authored story, not entirely a sandbox.
And there is no value judgement here, either. Both are valuable and necessary components of the food economy. But they are not the same thing, no matter how many surface similarities they have. You would never mistake the one for the other.
The experience isn't the story. The story is the story.