The problem existing, not specific to this case, is probably not new; it has existed for many years.
From my previous testing on Windows 2000 a long time ago:
Windows Media Player since, I believe, after version 7 have not been able to be correctly uninstalled. Also an instalation attempted after "uninstaling" a later version of Windows Media Player than the one being installed will not result in a correctly funtioning Windows Media Player (although it may still run and play media).
Microsoft does not seem to address the problem.
A desired version of Windows Media Player can be made to function correctly on Windows 2000 (probably also applies to Windows XP) by modifying registry information and files on the file system.
I have multiple times in the past successfully installed an earlier version of Windows Media Player and had it function correctly. Unfortunately, I have forgotten what specific modifications need to be made to the Windows registry and files to correctly have Windows Media Player functioning (not simple; quite a complex mod). I regret not documenting my findings.