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Yes, the 2D grid level is rendered as a texture and mapped onto several simple 2×1 strip meshes (made with Blender), and the shader bends each strip into the ring and applies the twist. Player movement and keys/doors logic run on the 2D layer, and the result is re-rendered to the texture every frame.

Thank you for playing my game, I'm glad you liked it.

I set up a camera for the 2D grid level and rendered its output onto these strips. The strips are then bent and twisted via a shader, using parameters like "left edge twist angle", "right edge twist angle", "segment count", "segment index" and etc.