Linux is not required for parallel processing algorithms.
OTOH, when it comes to implementing those algorithms, there are a number of reasons why Linux/Unix tends to be preferred by the implementers. First off, many of the implementers are on tight budgets and Linux is a lot cheaper than, e.g., MS Windows. Sure, a lot, probably even most of the PCs you can get your hands on already have MS Windows licensed and loaded, but the cheap (read older) PCs will probably have a variety of older, less secure and less capable versions of MSW on them, not to mention that MSW is a relative resource hog compared to Linux/Unix. For one thing, you can load and run Linux (or Unix) without the resource-intensive graphical user environment that is required by Microsoft. For another, Linux is a lot better optimized for performance. Windows always seems to be built to run on the next generation of hardware from when that version was introduced, that is, it always has been a resource hog. The result is that you can use older and cheaper boxes efficiently with Linux than you can with Windows.
For another thing, many of the parallel programs have been developed as open-source freeware by people who believe in doing that sort of thing. Linux just seems like a more natural choice to people who want to share their code.
But probably the most critical reason is that it's just a lot easier to develop parallel, multi-computer code on Linux/Unix because the protocols for network communication are a lot clearer on Linux/Unix. You can do network software in Windows, but everything gets all tied up with Microsoft's implementations of everything and is subject to change at Microsoft's whim. Whereas, on Linux/Unix, there are real standards and it's easy to work with them. I have not really done anything significant with parallel processing, but I have had some occasions to need interprocess communication between different processes running on different Unix boxes -- it's easy! I don't doubt that I could (eventually) manage to do something comparable on Windows, but doubt that it would be as easy.
Best Regards,
Paul