So I too ran into this problem some time ago and thought it was solved forever with the KB3099229 update as mentioned by RickGoemans.
However, the recently released Windows anniversary update seemed to have uninstalled KB3010081 and KB3099229 for me (they no longer showed up in Windows' installed updates list). Reinstalling KB3099229 didn't seem to have any effect (Media Player was still not shown in the features list of Windows)...
After a lot of googling it turns out there's an even newer version of the Media Pack: KB3133719 (available here: https://www.microsoft.com/en-us/download/details.aspx?id=53356 ).
So to sum up, there’s now three updates that supposedly fix this problem:
KB3010081
KB3099229
KB3133719