Seems like it's just taking a "flat world" and mapping to cylindrical coordinates. Essentially wrapping the world on a cylinder. I did something similar with a flat world, but I wrapped it onto a sphere:

The way I did it for a sphere is similar to the way you'd do it for a cylinder. Choose a suitable radius (ρ or "rho" in cylindrical coordinates) for your world. For each vertex, take the XZ coordinates of your world (assuming Y is height), then covert to cylindrical coordinates using the XZ and radius plus Y. If you don't add the Y, you'll get a flat cylinder. Then convert back to Cartesian coordinates to draw in game.