This should be well within the capabilities of ordinary photo process, even back then.
The traces do not disappear, they go into the pads just as you would expect.
For example the one highlighted with the blue arrow goes to the pad immediately above the arrow.
What is unusual is the design restrictions placed on this.
I know nothing about how these were designed but the way the traces are routed leads me to believe they were drawn automatically with some early PC software rather than by hand.
It looks to me as if the software worked with something similar to a netlist that made connections between a grid of pads according to some predetermined rules on how to route a trace.
This would be possible with very limited processing and especially graphical display power, possibly even in something more similar to a spreadsheet form rather that the "visual" CAD we are used to now.
Again this is just speculation.
I do not know if there was a process advantage to always having all the holes in place.
Perhaps the pattern of holes was pre-punched on the raw stock and through hole plated beforehand.
This way the board manufacturing would completely avoid those more complicated steps.
I have seen boards before that seemed to have an abundance of unnecessary on-grid square pads similar to this in old computers, but never ones with 100% pad fill like a breadboard.
ST