Yahoo! Maybe!
How do I upgrade to Office 2016 if I have an Office 365 subscription?
https://support.office.com/en-us/article/How-do-I-upgrade-to-Office-2016-if-I-have-an-Office-365-subscription-ee68f6cf-422f-464a-82ec-385f65391350?ui=en-US&rs=en-US&ad=US
No Revert back to 2013 from 2016! (see link above)
Sorry, “upgrading” to 2016 is a one-way trip, like falling into a black-hole <grin>
Office 2013 is no longer available at all (bad luck if you wanted it for compatibility or just familiarity).
Change in Policy - Maybe Rollback - "Unsupported version of Microsoft Exchange" error when you use Outlook 2016 to connect an Exchange 2007 account”
https://support.microsoft.com/en-us/kb/3093039
This article provides you with a way to bludgeon MS Support into giving Office 2013 back! YAYYY!
I just saw this question and reply.
http://answers.microsoft.com/en-us/office/forum/office\_2016-outlook/rolling-back-to-2013-from-2016/edda2c54-de95-446f-a306-59c688f15899
So if you contact MS support and quote the MS KB article you may be able to get 2013 back! YAY!
https://community.office365.com/en-us/f/172/t/409681