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).