Who is that in Dark Twist Square and how are they related to Gen Urobuchi's work?
That's M. Night Shyamalan, a film director and screenwriter known for making films with supernatural plots and twist endings. Some examples of films he has created are The Sixth Sense, Signs, and The Last Airbender. There are a lot of memes about his signature plot twists. 

(Incidentally, I became first aware of M. Night Shyamalan memes from LittleKuriboh's Spoof Movie no Jutsu~, an abridged parody of the first Naruto movie.)

As far as I know, the only connection between Gen Urobuchi and M. Night Shyamalan is the plot twists thing, and nothing more than that.