I don't think Windows will die anytime soon. Yes, the traditional Windows desktop will die eventually. This is why Microsoft probably makes such a strong play with Azure and Office 365. But Microsoft can just continue to sell Windows + Blink-based Edge as a modern desktop for web apps that also has support for legacy win32 applications for those companies and individuals that need it.
Building a compat layer on top of Linux seems to make little sense. It will be a huge time investment and while desktop Linux is great for developers, the whole ecosystem is to volatile for most end users. Plus the Linux graphics stack is still not where it needs to be.
Whether they'll acquire a Linux distributor is a completely separate question for me. I think it makes sense to acquire know-how and some influence for Linux on Azure. On the other hand, maybe they don't want to upset other Linux vendors. Oracle, Red Hat, and SUSE are typically used on expensive SAP/Oracle deployments. In fact, they were even SUSE resellers one day ;) .
I've seen this parroted before, no evidence to support this opinion.