I am sorry to say the only "fix" is to contact MS Support. MS has announced a free upgrade from Office 2013 to 2016. The problem is they forgot to mention it to the people working on the support lines. So you can expect to spend MANY hours on the phone trying
to find someone who is willing to help you. You can also expect to be hung up on more than once ...
You have my condolences, and I wish you good luck ...
Special offer for customers with Office 2016 and Office 2013 standalone applications - Free Upgrade
https://support.office.com/en-us/article/Special-offer-for-customers-with-Office-2016-and-Office-2013-standalone-applications-c32e3cad-e935-4163-a44f-50d896e10bbc
https://support.office.com/en-us/article/-We-need-to-remove-some-older-apps-error-a225347f-e102-4ea6-9796-5d1ac5220c3b
<SNIP>
Office 2016 and standalone Office 2013 applications (purchased separately via a retailer and not part of a suite of applications) cannot be installed on the same device. To resolve this issue, you’ll need to upgrade your standalone applications to the Office
2016 version of the products. Please contact the Microsoft Answer Desk to obtain a free upgrade for your qualifying standalone applications.
This offer is subject to the following terms and conditions:
- Offer expires June 30, 2016.
</SNIP>
<snip https://answers.microsoft.com/en-us/office/forum/office_365hp-visio/office-2016-uninstalls-my-visio-2013/11954b21-d1bd-42ce-82b2-d3178ae00ca6 >
Yay..today they finally sent me my link to Visio and Project 2016.
You do have to persevere. It took me about ten tries over 5 days with the answer desk online chat before they escalated it. Within 48 hrs they called and emailed me the links.
</snip>