The only way it's going to make any difference is if you can run the ffull Linux GUI in Windows .. and if that happens, I couldn't care less if people get exposed to Linux (or Peppermint) via Windows .. they're still getting exposed.
At the end of the day, those that prefer Linux will ditch Windows, those that prefer Windows will stick with it, and those that want both will either run a Linux distro under Windows (as they might now with a VM or previously with WUBI) or realise dual booting is the best couurse.
In all cases nothing changes except a few (and I do mean few, most won't care) will get exposed to Linux .. which can only be a good thing.
I don't see this as a threat at all .. in fact
a) Microsoft are showing little interest in running GUI Linux.
and even better
b) They appear to be loosing interest in Windows altogether:
http://money.cnn.com/2018/03/29/news/companies/microsoft-restructuring-windows/index.htmlIf you remember, I said ages ago that at some point Windows would become a financially unviable proposition, Microsoft would attempt to turn it into a service, then drop it, and Linux would be what's left (eventually winning the desktop by resignation) .. I still hold true to this belief

The desktop market is shrinking to the point where Microsofts 'proprietary' development model will no longer be worth the input, and other services will become much more attractive propositions for them to concentrate on.
[EDIT]
A question has just dawned on me...
I wonder if this "Linux subsystem" is more about preparatory work for ditching Windows altogether .. in a more "look you can control your old Windows server from Linux", you no longer need desktop Windows.
(probably not, but something to think about

)
[EDIT2]
Much more likely that they're planning on ditching Windows, and just selling licenses for Linux on Azure (as suggested by that article) and this is just a way to start the ball rolling.
[EDIT3]
Heck they've even SAID it .. "Windows 10 will be the last version of Windows" .. then left it for people to interpret that as they chose.
Laying the groundwork ?