How does IIS identify that request is MVC or ASP.NET request?

IIS doesn't know; ASP.NET knows via HTTP Handlers

Both WebForms and MVC are built on top of ASP.NET, and both use HTTP Handlers to deal with per-request execution:

• WebForms has .aspx files mapped to the PageHandlerFactory
• MVC integrates into the Routing infrastructure as an IRouteHandler implementation. Routes is notified of requests via the UrlRoutingHandler