It does look like some form of dedicated system.

On the plus side for you, it looks like step/dir servo drives (note that on your photo of the motor wiring, each axis has XA/YA and DIR). This gives you a good choice of possible controllers, although you'll need to find manuals for the drives to check that they do take 5V step/dir, as some may require 12/24V signals. I notice the top connectors are marked GND & 5V, so I'd assume the drives use 5V, but it's easier to find a manual and check now, than have to change things later.

I'd guess one of the SSR outputs at the top is what should enable the drives.

One thing that stands out, is why is the E-Stop led not lit on the inputs?

From what I can see in your photos, this only needs a relatively simple controller to get going, although it will most likely have to be 24V capable (there were some 24V capable BOBs discussed recently, but I can't remember what they were).

My suggestion would be start tracing wiring from the control board, make a list of where it goes to, and what voltage it needs (if known).