No you don't need a web server, GIS server runs on port 6080, so you can access your GIS services on this port e.g. http://servername:6080/arcgis/rest/services
Oh in that case you'll need to install the web adaptor. It's trying to access a server called "GM2", which isn't public. So I think you'll need to install the web adaptor on your web server (http://gisinsight.com), so this will forward requests to your gis server (GM2)