Heyo! Just finished whipping this up!
Basically it's a twisty puzzle with two layers of corner turning: the standard "3x3x3" turn (aka. Trajber's Octahedron), and the shallower hyperbolic cuts, which form those non-standard cuts that meet together at the centre of each face (the wide gaps in the puzzle are caused by filleting these; similar to the mass-produced "Flowerminx").
On top of that, 4 of the 8 faces have 3 bandaged pieces (i.e. pieces that have been fused together). Two of those exhibit a "clockwise" pattern and the other two an "anti-clockwise" pattern. These should restrict moves in certain permutations, thus adding to the difficulty of the puzzle. (I've also checked to make sure they do not restrict too many moves.)
I will admit that this has never been printed before, but it uses the shell mechanism: one of the standard approaches for designing twisty puzzles. Apart from the hyperbolic cuts, the mechanism resembles the mass-produced 3x3x3 Crazy Cubes. In other words, it should work.
Now for the part where it somehow fulfils the design brief... To be honest, I'm doing this for the sake of seeing another twisty puzzle in the competition, but I will make my case. It's probably going to be more of a "wow twisty puzzles are really cool and you should actually look into them" kind of promo. :V
It's important to note that when the Rubik's Cube came to fruition, many were not only engrossed in developing the fastest and easiest algorithms to restore it, but were also fascinated with its inner workings. Nowadays, it cannot be denied that the existence of most new twisty puzzles heavily relies on 3D printing: both for pushing the limits of their already intricate mechanisms, and finding optimal placements of cuts and screws (or even lack of screws) to make these even feasible for mass production.
A few minutes of browsing through the Twisty Puzzles forum can already attest to this. Geared puzzles, sliding puzzles, higher-ordered puzzles (like that recent 33x33x33), deep-cut puzzles which somehow hold on to so many moving parts, geometries of jumbling puzzles, etc... Should probably watch this too for a brief overview of a classic: https://www.youtube.com/watch?v=83a_DX8WDe8
With such possibilities, it can be easily seen how the challenge has been brought to the "next level". For twisty puzzlers, the puzzle is often both the solution, and the puzzle design itself.
Of course, this only speaks for the category in general and not the specific puzzle here. I'll admit it is quite basic, but it does exhibit hyperbolic cuts, which enable visually impossible turns to work. I was hoping to fix the fillets as mentioned earlier so that this would be more apparent, but I ran out of time. Better examples can be seen here:
Such cuts almost definitely need 3D printing to achieve. Before that, there were very few puzzles that featured these cuts, and virtually all of those were extension mods using plastic sheeting on existing puzzles. I guess that's the only claim this puzzle has in showing the advantages of 3D printing.