I would say that you can see the lynx.iotopen.se portal as a MQTT Broker. The MQTT broker one component of the IoT Open platform. Every unit that connect to this broker can communicate over it are considered a MQTT-client. So the Z-wave gateway in this case is a MQTT client. However, if the Z-wave gateway as an IoT Open edge-client it also has a local MQTT Broker to witch lokal MQTT-clients can connect. Those clients can communication locally or/and globaly via IoT Open.
A subscriber is someone that listens (subscribes) to certain topics on the MQTT broker (and is a MQTT client according to the discussion above).
A publisher is someone that sends messages to certain topics int the MQTT broker (and also a MQTT client according to the discussion above)