I tried downloading strongholder crusader HD today on my mac and when I opened it it gave me a "file is damaged" error message. Has anyone else had this problem / know what to do about it? Thanks in advance!

a) Redownload the game using the newest version of the GOG Downloader:
https://secure.gog.com/downloader
To download, make sure the "GOG.com Downloader mode" is switched to ON before clicking the "Game installer" button. After the download is complete, reinstall the game.
b) Use this workaround if using the Download didn't help:
- Go to Applications -> Terminal
- Type in:
xattr -d com.apple.quarantine
but don't press Enter.
- Drag the application to the Terminal window, this should add the path.
- Press Enter.

Redownloading usually works for me (as posted by triock above).

Another thing I have tried which works sometimes is to go to "Security & Privacy" (in System Preferences) and change "Allow apps downloaded from:" to "Anywhere". I have no idea why this works, after all it's not fixing the file, but I have had success with it.

(ETA: I don't actually have Stronghold Crusader HD in my library, I am just talking generally for various games).

It's the second solution in the FAQ (Can help even without that error message):