Is it a Ninja Theory thing or just coincidence?

Maybe it's like their signature? Just like it's Sonic Team's signature to make bad games... 

I don't know, but I hate it. 
 
And is that second shot from some Ninja Theory game's concept art? If so, then I guess that officially makes it a "thing."

" I don't know, but I hate it.  And is that second shot from some Ninja Theory game's concept art? If so, then I guess that officially makes it a "thing." "

Face paint is typically used to show tribal characters, you won't see Dante with face paint.

See, this is where some knowledge needs dropping. The story of Enslaved is an adaptation on an old chinese story 'Journey to the West'. Monkey's design is based on the illustrations of the main character (also called monkey) from that original story. The recent opera that Damon Albarn and Jamie Hewlett did of the original story also has a very similar design for their version of Monkey, see here and here. The use of facepaint on NT characters may be there in a classic theatrical sense, as make-up to imply animal characteristics.