Links: Yes, Avast has a false positive on hitman.exe, happened to me yesterday when I finished the download and the setup file got scanned. If the antivirus is configured to take automatic action, it probably removed or quarantined the file (same effect) and you didn't even notice.
The solution above is ok, but it is better to disable automatic actions if you know what you are doing. If you do, you can even report the file as a false positive to Avast's servers and prevent this to happen to more people.
--edit--
One more thing, exclusions should be kept at file level (exclude hitman.exe instead of the GOG folder or even the game's folder). Excluding folders can get tricky and is dangerous in the long run.
After going through the support from Gog, I realized it was Avast. When I tried to install the game, I kept getting a MoveFile failed error. I had to disable avast to install it. Then when I tried to play the game after enabling avast, my game wouldn't start. apparently avast would remove my game.
Is this a problem with Avast or is it a problem with the game?