It is stated that MQTT usually runs over TCP/IP. I found a figure below and I was confused.
I know that TCP/IP is a set of communications protocols, but not only means 'TCP' and "IP' these two protocols. Then what is the meaning of MQTT 'run over' TCP/IP? Can I say that the three-way handshake , retransmission, and error-detection of TCP allows ordered, lossless connections of MQTT?
Then what is the meaning of MQTT 'run over' TCP/IP?
The table in your post is actually a presentation of the OSI-model. In that model there are layers of protocols, where protocols of a layer rely on protocols from layers below. So the MQTT (layer 7) relies ('run over') on TCP/IP stack (layer 6 and below).
can I interpret that the 'other network protocols that provide ordered, lossless, bi-directional connections' which MQTT runs over are the protocols not included in TCP/IP models?
Yes. Zigbee, for example.
can I say that the three-way handshake , retransmission, and error-detection of TCP allows ordered, lossless connections of MQTT?
Well, "ordered, lossless connections" are probably ensured not only by features of TCP, but also by mechanisms belonging to MQTT protocol itself.