Sarcasm? I imagine that they're not emulating the Linux Kernel on Windows... From what I've gathered from job postings and whatnot, their virtualization system is in line with AWS's (Xen) on Linux.
When you're running Linux on Azure, it's via Hyper-V or rather the Azure flavored form of it. Windows is very much the core of Azure.
Azure Cloud Switch does use Linux - on metal I believe so no virtualization.
Edit: a word
My source: I work for MSFT, not on Azure but I work with their team a lot and I used to work on Windows.