Half-Life mumble mumble. There are practically no cutscenes, and the story is told by what the characters speak (to either the player character or to each other), what happens in the world, and sometimes by what you find in the world. When Half-Life first came out, I had too little experience with games to understand but apparently that kind of storytelling was revolutionary back then. Nowadays it's of course not that rare anymore.
I've recently been playing Crusader Kings II, and I feel like it's a good fit in this thread. It's full of emergent stories, such as this one. Basically there's politics, relationships between people, events, and decisions, and all that stuff, which can create some interesting narratives - or not, if you'd rather play safe and lead a boring life.
