verify your game files, then go to the Sniper Elite 3 install folder, open the CommonRedist folder, scroll down till you see DXSETUP(.exe). Also make sure you have a system that can run DX11, you'll need at least an nVidia GTX 6xx or newer, or an AMD 76xx or better.
Also clean your system cache...
open your C:\windows\temp\ and delete ALL the files in it
also open c:\users\<username>\appdata\local\temp\ and delete all the files in it.
then open my computer,
right click on your c: drive and select properties,
then on the "General" tab, under the image of the disk usage,
click on disk clean up,
once it finishes calculating...in the top box, put a check mark in all the options
and click okay in the bottom,
a new window will pop-up asking "Are you sure you want to permenenatly delete these files?"
click on delete files (or the equivilant).
close all open windows,
try launching the game again from steam.