uninstall and re-install client integration plug-in.
use Google Chrome or Mozilla Firefox, see if this helps.
Also allow plug-in to use local resources, this might come as popup message.
I have found to be broken in vSphere 6.
Oddly enough, if you type the username: DOMAIN\user or email@example.com, it is possible to log-in
Thanks for the suggestion - Uninstall / Reinstall didn't help unfortunately. I can login using the method that unsichtbare said but the "Use Windows session authentication" checkbox should work.
I'll open a ticket and post the results here.