It turned out to be the fullscreen DPI bug, which occasionally affects Windows 8 (and I guess 10). Since it's fairly rare it's probably graphics driver specific. The symptoms are that either part of the screen is cut off, or the mouse cursor position doesn't match up to what is being shown on the screen, which makes clicking on things rather difficult.
The only known workaround is to run the game in windowed mode, where it works fine. There are probably some system settings that can be tweaked to avoid it but I've never encountered it personally.