No, powershell runs on Linux, it just sucks because it wants objects and everything on *nix speaks streams of text.

PowerShell works on Windows because of WMI, to a first approximation.

Because Windows is tied together through APIs and databases and not text files (unlike Linux), everything is text is not as useful as something that can talk objects. And a lot of Windows is object oriented, from the window message dispatching system through COM and down to NT's object manager.