You are a lone adventurer in a strange, non-Euclidean world. Gather as much treasure as you can before the nasty monsters get you. Explore several different worlds, each with its own unique treasures, enemies, and terrain obstacles. The twist is the unusual geometry of the world: it is one of just few games which takes place on a hyperbolic plane. See the videos (on the game's website) to see the unique perspective available on the hyperboloid.
This video shows gameplay of HyperRogue III. It shows all the lands available, but does not try to win the game (the final message shows what remains... this requires some spoily tactics, I want players to discover them for themselves instead of watching the video). I wanted the video to be relatively short, so it is also a speed run of sort.