When I start the game I get a 404 files not found error. I've uninstalled and reinstalled a couple of times. I downloaded the replacement executable podcat and copied it to the game folder. I renamed the old hoi3 launcher file as "hoi3-old" and renamed the podcat as "hoi3." I am running Windows 10 64-bit. GOG says it may be weeks before support responds.
I have this one suggestion after doing a search:
Navigate to your hoi3 installation. I would think though it is actually in Documents as that folder does not get deleted when you reinstall. Documents/Paradox Interactive/Hearts of Iron III/map. The other location is where you installed it.
Open file "map".
Within that file is another file labelled "cache".
Delete everything within that folder.
Restart your copy of hoi3. The cache will be reconstructed. This may
take a few minutes.
Sometimes the game will get corrupted when you first start it up.