It should be possible to use a website or a web application project. In the example, from the link you posted, they use a predefined template for ASP.Net MVC Web Applications. This has several advantages - it establishes a structure and other resources for you - it is an effective template.
For the purpose of the tutorial, why don't you just configure the application this way? If you have already written the code, you can simply import it into a new application.
For future projects, you might think about what works best for your needs. Besides structure, there are some other key differences between a web application and a website design.
MSDN conveniently provides the differences here:
http://msdn.microsoft.com/en-us/library/dd547590.aspx
If you find that you want to use the functions of the web application, then the link you published is in order. You will need to reorganize your links, etc. Etc., But the process is quite simple (but not painless).
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