Visio for O365 and Office Standart 2016

Office Standard 2016 (MSI) and Visio for Office 365 (2016 - Click-to-Run) won't coexist unfortunately this is a known, frustrating, issue as you have discovered:  

"You can’t install two products together that have the same version but use different installation technologies."

In the instance, you have described you would have to downgrade to Office 2013 Standard or use the 2013 version of Visio Pro for Office 365.  Another option would be to use Office 365 ProPlus if that's an option or buy Visio 2016 (MSI) instead, via Volume Licence.  Any of these would coexist.  More details are available here - Supported scenarios for installing different versions of Office, Visio, and Project on the same computer.

Here are two scenarios that expand on this:

The two general rules for which installation scenarios are supported and provides some examples

The way we do it, is we buy volume licenced versions of Visio 2016 (or Project 2016) and deploy this alongside Office 365 ProPlus using ODT.  This is a special configuration, which requires KMS activations but it works well for us. More details - Use the Office Deployment Tool to install volume licensed editions of Visio 2016 and Project 2016.

 Here is a summary:

Supported installation scenarios for Visio 2016

Hope that helps a bit.