It appears the straps are used to hold stuff onto them, in the picture you included the guy on the right has what appears to be a knife handle above his left shoulder. You can actually see that clearer in the below picture and the straps also have a bag at the bottom of them.
Also in this next picture you can see that the straps have a bag on them covering the whole of the back.
In the book, leather only appears in the form of a loop with which Ben is tied to a pole and forced into banishment. There is also no mention of vests or belts. When the Runners go out into the Maze, they carry backpacks full of supplies:
Minho continued talking. "Here's a backpack, water bottles, lunch pack, some shorts and T-shirts, other stuff."
From the lack of these contraptions in the book, I would assume that they have replaced the backbacks in the movie as part of the visual design. They have no other purpose than to look cool (or stupid, depending on your tastes).