Definitely can be told through environment or any narrative elements, really.

The very fact that a player moves to the left instead of to the right to progress through the game can already tell something. Maybe is a revenant story.

Or the fact that the player can fall up to 2 seconds before taking falling damage, this can tell a story as well: the character is fragile and is on a path to become stronger?

The important aspect of the Story Criterea is judging if this underlying narrative progression: is this revenant good? What happened prior to it? Do players end up understanding the events that proceed the game when they finish it? Does this character actually go through a tranaformation and becomes stronger? How? What happened?

This is the kind of things I wanted to entice: how are you going to progress the player through the game events (the medium doesn't matter much, though there’s no direct "punishment" for using cheap approaches like text to tell the story as well).