The story is a bit vague
If I understand this correctly, they're running Docker on top of Linux on top of Windows on top of Hyper-V. That's quite a contraption, I must say.
Both the story and Microsoft are a bit vague as to whether they are using Windows as part of the Azure set-up, or if it's only present if you're stuck with a Windows machine for development use. In other words, we don't know if this is a kludge that is only used for development, or whether they really think that people will use this in production.
The Microsoft post on GitHub (referenced in the Microsoft blog post) also says that Microsoft are running into some pretty fundamental problems in trying to get Docker to run directly on Windows. Docker by its nature as a container system, uses some pretty fundamental features of Linux which don't translate to Windows. I have to wonder if Microsoft is on a hiding to nowhere with this effort. There will always be unexpected "gotchas" when trying to run a Docker package directly on Windows.
Changing Docker to only offer "lowest common denominator" features isn't a realistic option either. Most cloud users will be running on Linux, and if Docker can't do the sorts of things which other container systems can, then few people will use it.
Given the above, Microsoft might be best advised to give up on the effort, and just recommend to their customers to run Linux directly on Azure, or directly on Hyper-V for local (non-cloud) installs.
Just like Microsoft has given up on making Windows Phone a major player and are now offering their software on Android and Apple iOS, they may need to re-position Windows as a "legacy" product so far as servers and cloud are concerned, and focus their efforts on offering software and services on top of Linux. The market is changing, and if they don't realize that and follow it, their server and cloud business may end up going the same way their phone OS business did.