The HardwareID you're looking for is located in another WMI Class. Once you have an instance of a Win32_NetworkAdapeter, you can select a Win32_PnpEntry using the PNPDeviceId. Here is a sample code that list all network adapters and their hardware id, if any:

        ManagementObjectSearcher adapterSearch = new ManagementObjectSearcher("root\\CIMV2", "SELECT * FROM Win32_NetworkAdapter");

        foreach (ManagementObject networkAdapter in adapterSearch.Get())
        {
            string pnpDeviceId = (string)networkAdapter["PNPDeviceID"];
            Console.WriteLine("Description  : {0}", networkAdapter["Description"]);
            Console.WriteLine(" PNPDeviceID : {0}", pnpDeviceId);

            if (string.IsNullOrEmpty(pnpDeviceId))
                continue;

            // make sure you escape the device string
            string txt = "SELECT * FROM win32_PNPEntity where DeviceID='" + pnpDeviceId.Replace("\\", "\\\\") + "'";
            ManagementObjectSearcher deviceSearch = new ManagementObjectSearcher("root\\CIMV2", txt);
            foreach (ManagementObject device in deviceSearch.Get())
            {
                string[] hardwareIds = (string[])device["HardWareID"];
                if ((hardwareIds != null) && (hardwareIds.Length > 0))
                {
                    Console.WriteLine(" HardWareID: {0}", hardwareIds[0]);
                }
            }
        }