What is the URL or web link you are attempting to Open with Windows Media Player? How are you opening the link, have you tried with a different web browser (ie. Firefox), or entered the URL in WMP?
To uninstall/install WMP in Windows 10
Search 'features' to directly open Windows Features.
You can toggle Windows Media Player to enable or disable. A system restart may be required for the changes.
I tried another browser, actually 2 (FireFox and Google Chrome) but stills shows 'Windows Media Player encountered a problem while downloading the file.' Restored twice with different dates, rebooted, used ''Troubledshoot'. I didn't see how to uninstall 'Windows Media Player', I saw Windows 8.1 version. I saw Windows 7 and 8.1. (might have missed it )