He (Guthrie) blogged a few times about evangelizing open source in Microsoft, and given today's news, he gained quite a bit of traction over the years. It also helped that ASP.NET MVC is a pretty sold web framework too.
While it's true that Microsoft was taking steps to open source products under Ballmer, it was despite him, not because of him. There was an incredible amount of red tape, dragging of heels and internal fear uncertainty and doubt. Even internal only projects to synchronize open source practices among divisions were an uphill battle. If anybody deserves credit for Microsoft's open source efforts at that time, it's Sam Ramji who should get the credit, not Ballmer.
From the outside, Microsoft under Nadella has all the stops removed. This all lines up with a quote that I heard from Nadella 3rd hand: "We [Microsoft] can either push the 'One Microsoft' vision, or we can make money."
It will never go away, there's too much code and money involved, but it won't be used for new projects.
I would interpret that statement as: it's on the way out.
WebForms and MVC and WebAPI were different stacks that ran on top of asp.net to deliver different functionality. WebForms is the old school stuff and was great at what it did (which was replicate the winforms ability so desktop developers could rapidly create webapps) and serves millions of businesses today.
WebForms is still being supported but now finally seems to be removed from future roadmap. MVC and WebAPI have been combined together now. The latest stack is ASP.NET MVC 6 running on top of ASP.NET 5 running on top of .NET framework 4.6
The layers are ASP.NET MVC 6 running on ASP.NET 5 (the web framework) running on .NET Framework 4.6 (the core libraries).