There are two things you can try:

1. After installing the game via Galaxy, exit Galaxy COMPLETELY by going to your system tray and right clicking on the Galaxy icon and selecting "Exit". Next, restart Galaxy and launch the game. If this doesn't work then try the next step:

2. Crysis has two Bin folders: Bin32 and Bin64. If restarting Galaxy and running the game after restarting does not work for you, then please navigate to either the Bin32 or Bin64 (depending on whether you have a 32-bit or 64-bit system) and run the Crysis.exe file within the Bin folder.

In the mean time, I urge the both of you in this thread to send in a Support ticket by following this link:

https://www.gog.com/support/contact/technical_issues_with_games/crysis

and selecting "Launching issues" as the problem type :)

quick check: could you please replace a current launcher in game folder with one from this link (make a backup just in case) :
https://drive.google.com/open?id=0B1BxsqzJbT1FRXRzekVlYjV2eU0 and see if that makes any difference?

Great, I'll update the game on Monday.
As for the long launching issue, I don't think there is anything on my end I can do, except passing it along to the Client team.

Is the file I linked to few posts earlier making any difference?