@ OP
Zeno Clash kind of fits the bill. It also includes the best melee combat in any FPS, a (weird) story, and a pretty dreamlike setting. I found it kind of difficult myself, though I'm not much of an first person shooter person myself, and even less of a first person melee one, so your mileage may vary. In any case it is for both PC, in its original edition, and for Xbox, in a kind of ultimate edition that has some extra stuff added. Watch
the trailer on YouTube, since we are at it.
Since you did not specify a genre I'll recommend Hellsinker too. It's, more or less, the king of bullet hell shooters, or at least one of those. It's surreal, frantic, very hard, and even includes a fair bit of non linearity, though not on a TWAIN level or anything like that, given you can face different bosses and patterns based on how you play and a bunch of different and pretty obscure variables. Also, you have four different characters and their differences go far beyond a different shooting pattern, as each has many different weapons and attacks that deeply change the experience and gameplay. It also has some very awesome music. Watch
this Shrine of Farewell video or
this Stage 6 video to see whether it is your thing or not. The audio on the second video is kind of crappy, though, so the OST on the Apostles of the Seed battle sounds much worse than it really is.
Those two aside give Devil May Cry 3 a chance, too, as what you are asking for is, more or less, it. It is fun, mindless, over the top, so very cool, and so totally awesome you will enjoy yourself even if you don't want to. It also can get pretty hardcore depending on what difficulty level you pick for it. If you enjoy it, but only if you enjoy it, give DMC 4 a try, too, given 3 is the better game, and 4 is basically a good for what it is game that can go up to be pretty enjoyable if you like the DMC style but will never be as awesome as 3. Also, if you like DMC 3 give Bayonetta a try.