Do Redirect Clients in RESTful App Paradigms Have to Be Web Apps?

I need to retrieve information from a web app that uses RESTful API and OAuth 2.0 for authorization. As part of the OAuth 2.0 process (in this instance) I need to supply a redirect URL for the server to respond to once access is authorized.

My question, does the application at the redirect URL need to be a web app? Do only web apps listen to web traffic?

My confusion / the reason I ask is that I know I can create a Windows Service app and using HTTPClient or similar class in this app I can make a web request to the web app that uses RESTful API.

This leads me to wonder if I NEED a web app to listen to the redirect URL or can I use the same Windows Service app and have IIS or whatever the webserver is, direct traffic from that redirect URL to my Windows Service app?

I am totally green when it comes to web technologies.