Thank you for your answer.
What I want to achieve is to control these industrial printers from a remote station through internet.
They will be installed let's say in the production line, connected to the same network.
I would like to control these printers from the head office in another location. The manager can change the messages to print for example. At the beginning, I though about Modbus, but I believe that these printers have their own protocol (please see the manual) that accepts ASCII type commands through TCP/IP.
According to the manual these printer boards allow to be controlled by an IP network, so theoretically you don't need the server in your picture but control all printers remotely. But on that remote site you need a computer that knows what exactly to send to the printers. I expect that you already have that component.
I still don't see where the Arduino is located in that setup but that may be caused by a lack of information from your side.