How to install Microsoft Edge on Windows Server 2016?

Microsoft Edge was removed from Windows Server 2016 during the release candidate stage. It cannot be installed on it either.

According to Microsoft:

The Long-Term Servicing Branch (LTSB) versions of Windows, including Windows Server 2016, don't include Microsoft Edge or many other Universal Windows Platform (UWP) apps. These apps and their services are frequently updated with new functionality, and can't be supported on systems running the LTSB operating systems. For customers who require the LTSB for specialized devices, we recommend using Internet Explorer 11.

— "Microsoft Edge requirements and language support". Microsoft Edge - Deployment Guide for IT Pros. Microsoft Corporation (27 July 2017) via Microsoft Docs.

The "Try Now" link on the web page you've found simply tries to invoke a hyperlink whose protocol is microsoft-edge:. Internet Explorer recognizes this protocol as belonging to a UWP and tries to invoke that app, but only after asking you. What you see in screenshot #3 is the result of that app (Microsoft Edge) not being installed.

Looks like MS recognized the folly in this and changed their minds, the beta version works for Server 2016 now.

The official beta version can be downloaded at https://www.microsoftedgeinsider.com/en-us/