It's a tall order. But while this may seem daunting if not impossible now, if there are going to be computer games in 2027 and 2037 etc. etc. we shouldn't scoff at the idea just because it might appear very difficult to pull off now. I'm an old school gamer myself and if I could have peered from my pc with 384k memory in the 80s playing line art games to what we have now, my mind would have been blown.
What you're talking about is potentially doable with a heavy thrust into procedural development and variation. Even now the land we inhabit in games can be wildly varied and tools are getting stronger and more detailed in order to make landscapes unique. Games like Borderland boast literally millions of guns made from combinations of pre-modelled pieces. Games like Spore (and to a lesser extent No Man's Sky) have shown that variation of form is wildly possible using rules that manipulate the 3d geometry and textures of the model.
What we don't yet have right now are really tried and true ways of making all that variation high quality. It's very easy to generate a lot of bland, uninspired content and not so easy to capture the spark of creativity that makes content unique. I suspect simulation and pattern matching AI may play a strong role here: For instance, a weapon that drops just for you that's really good at dealing with poison and very bad at fending off fire, created as a table-top game master might because the game knows in advance that the bulk of your quests will lead you into the Toxic Swamp where there's so many venomous monsters but lots of water to douse fire. It can possibly feel as if the item was not just made for you, but that there's somebody out there looking out for you... quite a compelling feeling when you're alone against a world of enemies. The game that manages to deeply embed this experience into the narrative of the game world itself (bestowed to you by a patron god, maybe) will not only make players feel special but possibly bind to the world at a deeply emotional level (which makes for transformational game experiences).
Setting aside the big challenge of quality assurance (maybe players QA, maybe some fitness testing is possible to weed bad stuff out) I think there may be challenging currents of basic psychology that could cause problems: It may be true that, psychologically, if everything is effectively unique, everything *MAY* effectively be the same. For this to make sense, we have to consider how we evaluate things as having the quality of good or bad (value-wise). If a sword is good, say, WHY is it good? We can only know based on comparison. If it's so good that it kills every enemy with one hit, how do we know that's not the function of the game (this game is too easy) versus you're holding awesomeness in your hands?
I think it's somewhat inescapable that without bad there can be no real measure of good. A rusty crap dagger that works on rats but almost gets you slaughtered by man-eating orcs makes pulling Excalibur out of the lake and lopping off orc heads with one hit a fantastically satisfying hero's arc. If you start out with Excalibur, even if it's unique and the only one... not so much.
I also think balance is important. In a social game, keeping up with the Jones can be a powerful motivator. If everybody rides around on more or less samey horses and suddenly you see someone fly by on a dragon, you'll likely say "how do I get that???" That psychological driver may act to force a need for more uniform, specific achievements/geometry/models/rewards etc, if for no other reason than to make the truly unique stand out.