strange, that shouldn't happen at all. I can't reproduce the problem, so all I can suggest atm is try reinstalling the game.
the missing optical drive is not causing the issue, since all gamefiles are in the gamefolder. i dont have one either and all GoG games run just fine.

I had this problem as well. I could still load save files but I could not start new missions anymore.
I deleted all the files for Settlers IV in the gog.com folder, and redownloaded the game. From the installer, I could click launch game when it was finished. Doing this allowed me to start the first mission again (all my save files were lost but I still have them as a backup somewhere else). Content, I quit the game. Later I tried starting it again, this time with the launcher from my desktop, and the same problem happened. So I have good reasons to believe this has to do with the launcher rather than the game itself. Strange, because earlier I was able to play this game. I'm gonna try some more stuff, when I find something that works, I'll let you know.

Right-click, Run as admin.

I think I fixed this by using S4_Main.exe in the /exe folder instead of S4.exe