But it WOULD run under Linux--if hosted in Azure. In that scenario, you'd still be able to leverage any Linux-specific code that you have in addition to .NET code.
Or, if Microsoft wanted to expand .NET to Linux deployments outside of Azure, they could just charge a license fee for the framework and not have any restriction on deployment. Sure, they wouldn't be able to charge a lot for it (at least not as much as a Windows Server license would be), but they could make a little something from it. Or they could build the revenue model into the tooling.
Or they could just make it all free, and make Azure so awesome that people would want to host their Docker containers there instead of anywhere else. That might be the case anyway for whoever wants to target .NET. I think most .NET developers deploying their applications in a virtualized environment might be more comfortable using Azure vs., say, AWS. IOW, they could make .NET for Linux run anywhere, but make the ease of creating Docker containers (that run .NET for Linux) so easy to do in Azure, that more people would opt for deploying on Azure than anywhere else.
If they did this, Microsoft could spend zero time creating a Windows-version of Docker and spend time transforming .NET into a cross-platform framework that competes with Java.
Microsoft could get a big jump on this by buying Xamarin. Plus they'd get all of the Android and iOS cross-platform goodness with it.
Like with Office I hope Microsoft makes the decision to extend .Net's reach to other Windows competing platforms rather than keeping it locked into Windows. While unleashing .Net may not enrich them as directly as Office I'm sure Azure could quickly become the dominant cloud platform if Microsoft makes it easy and inexpensive for devs to publish their stuff and target & support as many devices as possible. Visual Studio and MSDN subscriptions would certainly get a bump in sales too if they integrated docker support better than other tools sets - yet allowing devs to continue to include their open-source tools in the tool chain like this.