They load fine here, my initial guess:

• No read permissions
• Hidden files
• File corruption

I would like to test these options. If it's the first option - how do I recognise no read permission and how do I change it?

https://www.windowscentral.com/how-take-owner … ders-windows-10
Check flag.set and fantasy.set

But it doesn't look like this on my computer. There is no tab titled "owner" in the security settings. I use Windows 7, not Windows 10.

How-To Geek have a similar guide and includes one part specific to Windows 7:
https://www.howtogeek.com/301768/how-to-take- … ers-in-windows/

In Windows 7, the “Advanced Security Settings” window has a separate “Owner” tab where you’ll make these changes. On that tab, click the “Edit” button and then click the “Other Users or Groups” button on the subsequent page.

I didn't help (I changed to something called "EU - Moderators", even though I'm the computer's only user). I even tried redownloading the game and the effect was the same: invisible tilesets.
Any other ideas? I don't want to be deprived of such a nice tileset as Fantasy!

That's starting to sound like you got it from an abandonware site which usually has missing or broken files. If the files were hidden you wouldn't be able to see both FANTASY.SET and FLAG.SET on the game folder.

Sorry, I can't help further.