Thanks, that is INDEED the old menu. (what folks who still have NONE selected would see). something is getting in the way of your update process....
When I select the 'None' option in the properties menu, which I did try just to see, it updated, the way you'd expect. You see the download progress across the bottom of Steam. When I set it back to the current release, it updated again, as it should. It does the same when I set it to 'release-candidate'. It updates, again as it should, or at least it appears to. It was left overnight after the last attempt last night.
I've also disabled the firewall just in case that was blocking. Didn't change.
Integrity/Validations all okay and the basic .txt file it leaves has one line in the log stating everything checked out properly.