I just bought a new laptop. I've done all the windows updates and it's now at build 15063.
ctrl+win+left/right changes the virtual desktop as expected.
ctrl+win+shift+left/right is supposed to move the current window to the next desktop, but it behaves as if I've pressed Win+arrows (snapping the window).
The keyboard supports n key rollover, so all the keypresses are being registered and sent to windows properley.