Plenty of people on Steam forum had it.
The thing with this game (and Anomaly games) is that the game always runs on a highest resolution available in the system, so if the resolution can not be displayed by the screen, you'll either get a black screen or a message that monitor can't handle it.
Here's a way to workaround it (hopefully it works as well on DRM-Free version):
1. Download
this config file and extract it.
2. Go to a folder:
%APPDATA%\11bitstudios\This War Of Mine or manually:
C:\Users\<your windows username>\AppData\Roaming\11bitstudios\This War Of Mine
3. Replace the existing config file with the one from PCGW.
4. Start the game. It should be working in a windowed mode. Do not enable fullscreen mode. Instead, if you really want to play on a fullscreen, use
Borderless Gaming to make the game run in borderless fullscreen windowed mode.
Hope this helps.