Hi CC Weedcontrol,
> ... so the Web AppBuilder for ArcGIS Developer Edition applications can be actually hosted on ArcGIS Server itself?
No, the Web AppBuilder apps can be hosted on the same machine where ArcGIS Server is installed on, but NOT within the Server site.
For example, you could have the ArcGIS Server component installed on machine A with Windows OS. Machine A might also have Windows IIS (web server) with the ArcGIS Web Adaptor installed. You could host the Web AppBuilder apps within IIS, for example at C:\inetpub\wwwroot
Hope this helps,