I just downloaded the downloader program for DD and was able to start a download of the game (though there could still be an issue with the server there, or Larian could be using different servers for DD and DKS).
Do you get the error downloading the download program from the 'Your Games' page on the Larian Vault website, or after running the download program? If the latter, try right clicking and running it as administrator, or see if your firewall (if installed/enabled) is blocking access (though a failure to connect would probably give a server not found error).
Try again, to see if the server just had a temporary problem (in the middle of an update, or something). If that doesn't help send an email to support@larian.com (though unfortunately it is a little after midnight there now, so you will not get a response for awhile.
