A "subfolder" in IIS is either a virtual directory or an application. To bind a DNS name to it convert to a web app in IIS (I think virtual directories work too but haven't done that in years). Then edit the bindings for the application and specify the DNS name(s) you want to bind to. IIS will then automatically send any requests with the matching DNS name to the application. You can also specify a binding for the root site if you want.
Default Web Site (binding: *) ::= myserver.company.org
App1 ::= myserver.company.org\app1
Default Web Site (binding: web.company.org) ::= web.company.org
App1 (binding: app.company.org) ::= app.company.org