There are two potential sources of this issue.
The file might be not marked as an executable. To change this, run terminal and navigate to the file's directory. Now execute the following command:
For example, for Stargunner installer:
chmod +x gog_stargunner_22.214.171.124.sh
for the start.sh launch script:
chmod +x start.sh
Then start it by typing:
If this does not resolve your issue, please refer to the following support thread for further solutions: