What OS are you running? 64 or 32 bit?
I just got it for my laptop on steam and it works like a charm.
Are your video drivers up to date?
I have exactly the same problem and no solution yet.
I had non-Steam version before and it worked fine. Just bought Steam version, uninstalled the old one. It does not start: exits immediately.
Solutions with atioglxx.dll didn't help.
Bethesda customer support has auto-response (try compatibility mode - I did, no difference).
My setup is Windows 10 Pro (64-bit of course), Radeon R9 390.
As I'm saying, non-Steam version worked just fine on my config. Tried to do some debugging but Steam returns error code, probably related to copy protection.