RE: user interface chromecast tab missing
Was driving me nuts how no one was confirming anything you said.
So I'm here to confirm that simply changing the "Local State" file (as noted here) will allow you to see the Chromecast option, but enabling it will do nothing.
Downloading your Profile files did enable it to work (zalex's file in case you missed the download link)
I wish I had a better understanding of which file I copied over enabled it to work so that the process could be simplified.
I wanted to go through the work of finding out which file fixed it, but it seems installing that ticked some other file and now I have Chromecast on a fresh install (so long as I change the Local State file).
So in conclusion, download Zalex's file, extract the contents, and copy everything in the red "Data" folder into you profile folder (Opera Menu -> About Opera, for me my path looked like this "C:\Users\my_username\AppData\Roaming\Opera Software")