subject line kinda says it all.
1Password Version: 6.6BETA-2 (660002)
Extension Version: 4.6.2
OS Version: 10.12.2 beta
Sync Type: dropbox
You won't be prompted for an administrator name/password if the account (e.g. an admin, in many cases) that's initiating the 1Password update already has sufficient permission to do it. This is generally true for installation and updating of other apps.
Hope that answers your question.
@sjk's comment is mostly right. If you had previously installed 1Password using the .pkg installer, which installs 1Password with proper /Applications folder permissions (typically root:wheel and 755 permissions) then you would be prompted for your admin password when installing updates.
Thanks for that bonus about the installer, Rudy. My response was focused on updating beta builds and its updater doesn't use that.
Thanks for the replies! - Roger
Glad that sjk and rudy were able to help. We're here if you need anything else.