how to show contextMenu when right-click on timeRange

You need to specify the context menu using .contextMenuSelection:

    dpc.contextMenuSelection = new DayPilot.Menu([
        {text: "New appointment", onclick: function (args) { 
            var start = this.source.start;
            var end = this.source.end;
            var resource = this.source.resource;
            var e = new DayPilot.Event({start: start, end: end, resource: resource, id: DayPilot.guid(), text: "New event"});
            dpc.events.add(e);
            dpc.clearSelection();
         } 
    }]);

See also the updated jsfiddle:

http://jsfiddle.net/p4qemLqr/2/

Thanks...Dan