So what I don't entirely understand is this. How can you make a game whose settings can exceed what the most advanced hardware can even render?
You mis-understood it, there is no game that our technology can't render. The problem is rendering it at a playable framerate.
The best example is the original Crysis. At the time the best single-GPU card was an 8800 GTX, but if you maxed-out all settings to Very High and resolution to 1920x1080 and AA to 8x, you would get around 10-15 fps - unplayable.
The GPU rendered everything just fine, it's just that the rendering was taking way too LONG. That's why they game was stamped with "graphics ahead of it's time", because to fully max out Crysis at
smooth framerates you needed a GPU setup that didn't exist at the time. CryEngine 2.0 could keep scaling as hardware became more powerful, you could keep ramping-up the polygons/shaders to absurdly high amounts.
CryEngine 3 is similar to that, though not as ridiculous because the fastest cards today (GTX690 and Ares) can run it fully-maxed at 1080p/8xAA at playable framerates. Hell, you can grab Titan SLI or 690 SLI and pretty much destroy the game at any resolution...if you've got $2000 to blow