With a Web Application Project, all the C# source code is compiled into dlls in the bin folder. mojoPortal web project actually is a Web Application Project.
What you are not understanding is that the "deploymentfiles" package is pre-compiled and has no C# source code, it is meant for production deployment, that is why VS treats it like web site project.
To work with the source code in Visual Studio, I recommend getting the source code download which has all the source code and Visual Studio solution files.
However, I will say, it will not currently run on Azure, it can use SqlAzure for the database, but the web code currently uses the file system which cannot be done on Azure, we need to first create a file system abstraction layer so we can implement support for running the web in the Azure cloud.
Hope it helps,