VS 2015 Preview missing "ASP.NET 5 Web Application" project type?

Visual Studio Ultimate 2015 Preview contains everything you need to create an ASP.NET 5 (vNext) web application. One additional generic option should be available that's not depicted in your question:

It's not entirely clear at this point, but choosing the generic web application option will present a few ASP.NET 5 (vNext) options that you're seeking in the following dialog:

I was having the same problem, except that unlike the accepted answer suggests, the ASP.NET Web Application was not on the list of templates at all.

I was able to get it to show up after following the instructions from this article.

1. From Visual Studio 2015: Tools -> Extensions and Updates
2. Select Online then click Visual Studio Gallery
3. Search for ASP.NET Project Templates and download the first result.
4. Go through installation process, relaunch Visual Studio, and Web Application should now be an option!

Alternately, you can download the templates directly here.

I believe this download actually is meant to install some other templates that I wasn't interested in, but installing them must have also installed the base template in the process. Either way, it worked for me.