Decoding coax signal
You appear to have the board out of an  OPK-CTL3 keyboard-video interface module.


It is intended for use with the Yokogawa Centum XL - micro XL distributed control system.  If you doubt that the linked item is your board, note that the picture shows the same designations for its BNC connector and the big multi-pin connector beside it, namely CN4 for the BNC and CN5 for the other one.  The board is also marked "OPK-CTL3" below "Yokogawa" in the upper left corner.

Given that the Yokogawa DCS is a networked system from the early 1990's, I would expect the BNC connector to be a 10MBit ethernet connector.  That makes decoding the signal to a data format easier, you just need an old ethernet card and a network sniffer such as WireShark.

Getting an old coax ethernet adapter to run on a modern PC might be a challenge as they were mostly ISA bus adapters, though there were later models for the PCI bus.  

You might be able to find new adapters for PCIe bus, though a quick look didn't find any.  

It will probably be easier to find an old 10MBit hub or switch that has RJ45 and coax connections and use that to connect your OPK-CTL3 to your modern ethernet card.

Given that it is ethernet, you'll probably want to avoid putting it on your normal network - Bob alone knows what adresses and/or protocols it uses.