I know it is not supported on Windows 8 or Windows Server 2012 yet but still is there any kind of workaround to install it on a Windows Server 2012 machine?
Edit: It's a 64-bit installation.
Since I solved this problem of mine, I felt obliged that I should list out the ways this problem, i.e. installing Zune Media Player on Windows Server 2012, can be fixed.
First of all, you can go here at Microsoft Answers and see the following (question+answer):
As answered by Dieter Bäumler at the same page of Microsoft Answers:
If both of the above methods don't work, as in my case, right-click zune-x64.msi and go to its properties and set its compatibility option as shown below and then run it: