Because players are always, always creating stories around their actions. We are creatures of pattern, creatures seeking for reason, and for us even the most non-narrative game has a beginning, a middle, and an end we can tell.
Even in games with explicit stories, the stories we tell aren't necessarily the ones that are written for us, which is the really fun part. In Fallout: New Vegas, for example, there's a clear story arc. It's a game with a potent, well-defined setting and very clearly-written quests. But I've been finding that the most potent moments are the ones I generate, not the ones the game does.
My favorite F:NV story so far? There I was, level 3, on the road trying to get to the next nearest town. I had a 9mm and a weathered 10mm and not much ammo for either. And every time I tried to go anywhere, I'd be surrounded by a mob of big, fatal, deadly radscorpions. Finally, in desperation, I clambered up a sloped rock. And very suddenly, realized a few things:
- I can climb this rock
- They can't climb up this rock
- They are all gathered together in one clump now, and
- I have dynamite.
The other really strong moment for me, so far (about 12 hours into the game, level 8-ish; I tend to explore the whole map and do every side quest before wrapping up the main arc) was in a town where a man, a sniper, is seeking vengeance on the person responsible for his wife's death, and asks you to help. You help by bringing someone in front of his sniper nest, and he does the rest.
Where that quest really got me was in the power given to the player character: as soon as you've accepted the quest, "Come with me to [sniper nest]" is a dialogue option for every single person in town. The game doesn't force you to make a right or wrong choice, or indeed any choice at all. The game leaves it completely up to the player to decide what kind of person her character is.
(For me, I was shocked at the thought of doing such a thing, and in fact even had trouble bringing the right person in... at least, until I found all the evidence. *shudder*)
So, yeah. Playing Fallout: New Vegas in that way that addicts with a shiny new toy do. And I don't at all mind that it's more of a Fallout 3: 2 than a Fallout 4, 'cause I really liked Fallout 3 and the real sequel will come soon enough!