You are a lone adventurer in a strange world, where geometry does not work in the expected way. Gather as much treasure as you can before the nasty monsters get you. Explore about 50 different worlds, each with its own unique treasures, enemies, and terrain obstacles. Your quest is to find the legendary treasure, the Orbs of Yendor. Collect one of them to win! Or just ignore your quest and collect smaller treasures.
The twist is the unique, unusual geometry of the world: it is one of just few games which takes place on the hyperbolic plane. Witness a grid composed of hexagons and heptagons, straight lines which seem to be parallel, but then they diverge and never cross, triangles whose angles add up to less than 180 degrees, how extremely unlikely is it to reach the same place twice, and how the world seems to be rotated when you do return. All this matters for the gameplay. The game is inspired by the roguelike genre (although in a very minimalist way), works of M. C. Escher, and by puzzle games such as Deadly Rooms of Death.
72 lands (72 in the free version), each with unique theme, mechanics, graphics, terrain features, native monsters, treasure type, and magical Orb power. The ultimate Hyperstone Quest requires you to get 10 treasures in each of the lands!
In many ways, HyperRogue is closer to boardgames like Chess, than to mainstream computer games -- except that its "chessboard" is a hyperbolic plane, with randomly generated features. Enemies move predictably, and most can be killed simply by moving into them -- however, they could kill your character with a single attack too! Even though the game disallows you from making moves which would lead to this immediately ("check" in Chess), fighting large groups is still a challenge.