Recently, my GOG Galaxy client failed to start (running Win 10). The behaviour was especially odd, as entry in the start menu simply became "unclickable". Normally, the start menu closes after a click, and then a crash dialog pops up. In this case, the start menu stayed open and nothing happened on click.

Anyways, going into the program folder C:\Program Files (x86)\GOG Galaxy and double-clicking on GalaxyClient.exe yielded an error: an issue with the side-by-side configuration. Further investigation into the event log (under Administrative Events) displayed the full error:

Activation context generation failed for "C:\Program Files (x86)\GOG Galaxy\GalaxyClient.exe". Dependent Assembly LIBCEF,language="*",processorArchitecture="x86",publicKeyToken="5e40110203010001",type="win32",version="7 4.1.19.0" could not be found. Please use sxstrace.exe for detailed diagnosis.

Going back to the program folder, I noticed that libcef.dll was renamed to libcef.dll.old. Renaming this file back to libcef.dll fixed all issues. I'm concluding that there was an error during client update that left the program files in an unexpected state.