I would not say that this type of storytelling is solely unique to games, for a large part Wall-E does storytelling with minimal storytelling. For games it goes back to the arcades.
I thought that this topic would be on environmental story telling. The sort of thing you see in games like Fallout, Dark Souls, Breath of the Wild, and others. Where games can tell story not by narration (words), but by things put into the environment for a player to discover.
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Through dream I travel, at lantern's call
To consume the flames of a kingdom's fall