Can't run SSMS as another user - requires elevated permissions

In case it helps anyone, I got it working by:

• Open the location to the shortcut, such as: C:\ProgramData\Microsoft\Windows\Start Menu\Programs\Microsoft SQL Server Tools 17
• Right-click > Properties > Compatibility >
• Select "Run this program as an administrator"
• Select the button "Change settings for all users" (THIS IS IMPORTANT)
• Again, select "Run this program as an administrator"
• Select "Okay", and 'Okay" again.

Hope it helps everyone.

Seems to be a known (unresolved) bug:

https://connect.microsoft.com/SQLServer/feedback/details/3009405/ssms-2016-fails-on-windows-10-version-1607-while-trying-to-execute-it-as-a-different-domain-user

SSMS 2014 still works fine so that's a workaround, or as @yahmoth555 suggested, use a different build of Windows.