Firek: Please try adding the game from a different browser and let us know if that changed anything.
I just tried firefox and IE 8. With firefox same problem as chrome, nothing happens, but with IE 8 two error boxes appear that say:
"gogdownloader://the_witcher_2_assassins_of_kings_au/is not a valid Win32 application."
and
"Unable to open this helper application for gogdownloader://the_witcher_2_assassins_of_kings_au/
The protocol specified in this address is not valid. Make sure the address is correct, and try again."
I've also tried deleting and redownloading the launcher, no luck there.