Game not launching

Hello @Dracheneisen, welcome to the forums. Based on the log you attached, you can see the following lines:

[00:00:00]: WARNING: Unsupported resolution 800x600.
[00:00:00]: ERROR: Error initializing OpenGl.  Your monitor does not support the specified resolutions or your video drivers do not support OpenGL ES 2.0.

Either make sure your drivers are up to date or go to Documents\Klei\DoNotStarveTogether and edit the client.ini file, once opened change the resolution to a resolution that your brother's monitor can display. Then save, after that start up DST again and see if it works. If that doesn't work, try and delete the client.ini and then start up DST again. If that still doesn't work, try and go to this location (Steam\SteamApps\common\Don't Starve Together Beta\bin) and right click dontstarve_steam.exe and under the compatibility tab enable run this program as administrator, then press Apply then Ok. After that start up DST again from Steam.

Hopefully the first method works, good luck. Cheers.

Drivers are up to date, we've already tried to edit the client.ini. But yesterday in the evening, the problem was for ALL his Steam games ( it wasn't when I sent you this request). Non-Steam games launched perfectly. Then he uninstalled and reinstalled Steam, no results. For now my brother will format his PC, hoping everything will going fine after that. We'll test the other methods if the problem is still here...

Anyway, thanks for the quick answer!