November 17 2017 Starting with Outlook version 1711 (build 16.0.8730), modern authentication is no longer a requirement and all Office 365 and Outlook.com users will have focused inbox capability in Outlook 2016 for Windows.
Several users (myself included), have noticed that Outlook desktop doesn't show the Focused and Other tabs for some Office 365 accounts. The installed version of Outlook supports Focused Inbox but it's not working. It's not that the Focused Inbox is turned off, the Focused Inbox button is missing from the View tab.
This happens when the tenant is not enabled for Modern Authentication. (Two-factor auth is not required on the accounts, but Modern Auth needs to be enabled on the tenant.)
The administrator will need to enable modern auth using PowerShell.
To check the setting or verify that the change was successful use this cmdlet:
Get-OrganizationConfig | ft name, *OAuth*
If OAuth2ClientProfileEnabled is False, the administrator can turn it on using this cmdlet:
After enabling modern auth, it may take several minutes for the focused inbox to be enabled, or you can restart Outlook and focused inbox should be available almost immediately.