Can I publish map services in geoserver like this?
You can't publish services exactly like that in GeoServer - the ArcGIS Server Feature Layer is Esri's proprietary implementation for sending vectors to the client.
If you're using GeoServer then as @user30184 noted you should look at a Web Feature Service to emulate the Esri Feature Layer.
The advantage of using ArcGIS Server's feature layer is that is has been built specifically by Esri, for seamless use within Esri's own APIs and other infrastructure. For example, you can create a FeatureLayer in the ArcGIS Server JS API, or edit the Feature Layer in an ArcMap session. The disadvantage is that you're locked into the Esri platform.
The advantage of the open standards like WMS and WFS is that you aren't locked into any particular vendor or platform. The disadvantage is that you may not get the full functionality of the ArcGIS Server Feature Layer.