https://support.office.com/en-us/article/Office-installed-with-Click-to-Run-and-Windows-Installer-on-same-computer-isn-t-supported-30775ef4-fa77-4f47-98fb-c5826a6926cd
from
https://social.technet.microsoft.com/Forums/ie/en-US/5483fbcc-cc2c-4564-a54f-1b239107ae1e/ms-project-standard-requirements-and-compatibility?forum=projectonline
..
Other Compatibility Issues
https://answers.microsoft.com/en-us/office/forum/office_365hp-project/office-365-and-project-2013-compatibility-issues/123a8a65-516d-48ed-8d7e-6104c3d74e72
..
This article says:
https://blogs.technet.microsoft.com/projectsupport/2015/09/23/project-2016-should-i-upgrade/
1. You cannot mix versions if you are running click to run installations – so upgrading an Office ProPlus click to run install from 2013 to 2016 will want to uninstall and 2013 click to run products it finds – such as Project and Visio for example. You will need to update to the 2016 for these too.
2. You cannot mix click to run with msi based installers of the same version. This means you cannot run Microsoft Office 365 ProPlus (which is click to run) with an MSI based installation of Project Professional 2016. You could either change to Project Pro for Office 365, or get a click to run Project Professional 2016.
3. You can mix different versions and different install technologies – so running Project Professional 2013 (msi installation) is fine with Microsoft Office 365 ProPlus (‘16’ level – click to run)
....
And THIS article
says the same thing
https://support.microsoft.com/en-us/help/2464297/a-microsoft-excel--word-or-powerpoint-file-does-not-open-because-of-in
The Click-to-Run and traditional MSI (Microsoft installer package) versions of Microsoft Office 2010 are not designed for use on the same computer. We recommend that you select one version to run on the computer to avoid problems such as those stated in this article.
For more information about Microsoft Office Click-to-Run and file associations, click the following article number to view the article in the Microsoft Knowledge Base:
982434 An overview of Microsoft Office Click-to-Run for Office 2010
