For a requirements example:
-This runs at 60 fps, 1080p, and runs 8xMSAA + FXAA. You can find this in the article linked in the OP.
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The Unreal Engine 4 tech demo runs at 1080p (90% of the time), 30fps, and only uses FXAA.
These two demos were run on the exact same card, and given frame setup time, you generally have about three times the resources to work at 30 fps despite it being only half the framerate. MSAA is also a pretty expensive form of anti-aliasing, which implies they had large amounts of processing power left over even at 60 fps/1080p in the Luminous demo.
A lot of what looks great in this demo, to the point many people prefer it over the Unreal Engine 4 showcase, is that Square Enix actually made really high end art assets that work well with their technology, whereas Epic just made a bunch of art assets that helped show off whatever features they were hoping to highlight. One of these was targeted at consumers (and their perception of Square Enix), while the other was mostly to show developers what UE4 does.