OK, thanks for the hint. Release hides the window. I thought I already tired it in this way before, but maybe I mixed up the gradle tasks. I though
runNativeMingwX64Release is simply the same as
packageMingwX64AppRelease + run it.
Also the icon works for Windows. So the note in the korge-hello-world README seems to be outdated. And it's good to know that you can provide a png instead of an ico file.
Note that windows executables doesn't have icons bundled. You can use ResourceHacker to add an icon to the executable for the moment. Later this will be done automatically.
Now I have my first real native kotlin game, great! If you want to include also the resources into the exe you can use WinRar to create an self extracting archive without dialogs which starts the exe after unzipping. I was impressed that zipping reduced the file size from 6,36 MB down to 1,82 MB. Say goodbye to JRE