Euclid Who?: HyperRogue
You are lost in a non-Euclidean space, constructed of tessellating patterns of shapes that recede into the distance in a way that simply doesn't make any sense. There are treasures here, from ice diamonds to rubies to spice, scattered through a double-handful of impossibly-constructed worlds. There are also monsters who can kill you with a touch, if you don't get them first. The more treasure you collect, the more monsters seek you out, but you need lots of treasure to find an Orb of Yendor before the monsters overwhelm you. Good luck. HyperRogue is a brilliant, dead-simple game that is not quite a Rogue-like and not quite anything else. Please keep in mind, when I say dead-simple, I mean that the art is cheap and the music... well, the music is quite nice, if not complex. In contrast, modeling a non-Euclidean space on my computer... I have no idea how simple that is.
You move through up to ten different worlds (plus one crossroads between them) that procedurally generate as you go, each with unique properties: In the ice world, your body heat will melt the walls; in the living cavern, walls move; in the running world, the ground falls away behind you. Enemies have unique properties as well. Though many have an AI that only charges you, the desert's indestructible sandworm moves once every two turns, and the jungle's murderous vines grow outward from a root one vine at a time, rotating around the center.
That's not all. Because one attack kills anything (with some exceptions), including you, the game plays on a checkmate principle: you can't make move anywhere a monster would kill you, and if you are being threatened, you must eliminate or escape that threat. And if there's no way out, you're dead. Checkmate.
A friend suggested that makes it a puzzle game, but it doesn't feel like a puzzle, it feels like you're running around a bizarre world trying not to die.
There's a lot of creativity in the variation of rules for the different worlds and and different monsters. That creativity is what takes a simple game with a non-Euclidean gimmick and makes it a smart game that's kept me playing for almost two hours, trying to find the key to unlock one of the Orbs of Yendor that I can find in Hell.
If you manage it, please tell me what's inside.
HyperRogue is available for $0.99 on Steam, or to play for free on the web.