Well, that's an issue with the game; it wasn't designed for that. I can only suggest playing at a lower resolution so that everything displays correctly. Besides, the game doesn't have extremely detailed textures.

How is it not supported? The 1920x1080 resolution is in the game's settings list; otherwise, I wouldn't have asked. Or is this just an obvious oversight by the developers? They added it to the list but didn't implement the support?

I don't care about the texture detail :o)
I want more to fit on the screen.

Added 4 minutes later
Clarification

I'm setting the resolution of 1920x1080 or any other not in the settings of my Windows screen, but in the settings within the game itself.
Start Menu - Settings - Video and Sound