Thanks for the tip. Found the solution using process monitor. While the game itself uses the registry paths mentioned above, the launcher checks this location
HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Electronic Arts\Electronic Arts\Command and Conquer 3 Kanes Wrath
for the String "InstallPath". After adding these keys and setting the correct directory, the game is found and online services work flawlessly.
As the registry paths are hardcoded, this problem could arise either by playing the game without installation from an external drive or by the way the registry is accessed by the launcher.
Thanks for your support!