After downloading and moving the file to my applications I tried to open the game and got this message "Stronghold Crusader Classic" is damaged and can't be opened. You should move it to the Trash. Any ideas?

Need more info,just exactly what did you do?

Maybe the file is corrupted.
Probably a download error.

Did you try re-downloading?

"moving the file to my applications" Is that a windows 10 thing?

It's always a good practice to write the platform you're on.
By the message I guess it's a Mac. I'm not a Mac user, but looks like in such cases downloading the file with a different browser, has solved similar problems for other games/users. Else you need to temporarily change your security settings.
Check these:
https://www.gog.com/forum/fallout_series/fallout_is_damaged_and_cant_be_opened_you_should_move_it_to_the_trash
https://www.gog.com/forum/avernum_series/avernum_6_is_damaged_and_cant_be_opened_you_should_move_it_to_the_trash
https://discussions.apple.com/thread/6792354?start=0&tstart=0

Are you sure you download the right file for your operating system and all of the necessary files as some games have more than one file.
Check your browser, the very very infrequent times I had a download issue, it said so on the browser download screen. If you used something else to download it then check that app.