Broadly speaking, it appears that games tell their stories in a spectrum bound by two extremes.
1) Linear Narrative
Think The Last Of Us, the Uncharted games, or some of the new God Of War games. These are largely linear stories that act as rollercoaster rides taking the player between preset narrative beats. If you were talking to a friend about a game like this, you’d say something like, “Have you reached the part where XYZ?”, when trying to discuss the story.
2) Freeform Narrative
Think Rimworld, Dwarf Fortress, Minecraft, or pretty much any multiplayer game. Here, preset stories are largely non-existent, and instead narrative is build by the player as they explore the game. It’s similar to how you might think about events in your real life through the lens of narrative. If you were talking to a friend about a game like this, you’d say something like, “You’ll never believe that XYZ happened last night!”, when trying to discuss the story.
Of course, most games exist on a spectrum between these two, but they largely tend to stick towards one end or another.