PoweredByJenga: Just did some checking, the offline installer do NOT work at all if you do not have an internet connection. They try to launch galaxy and that works but obviously fails to connect and fails to re-download gain.
This needs to be flagged to a wider GOG community.
Please double-check that you are running the correct offline setup files.
The offline installer of Crysis Warhead (English, Windows) consists of 3 files:
setup_crysis_warhead_2.0.0.5.exe
setup_crysis_warhead_2.0.0.5-1.bin
setup_crysis_warhead_2.0.0.5-2.bin
The EXE file itself has a size of 27,367,288 bytes.
If the file is named/ sized differently, you probably clicked on the "wrong" download... (see Dark Art's explanation above)