Welcome (even though you joined VCFED in 2013). You are still under moderation of course...
I am guessing some sort of interface card between the computer and the outside world. Maybe additional serial or parallel ports, or raw TTL I/O ports? Although for serial interfaces I would expect a 40 pin UART to be present - so strike that idea!
The green card is only used for the gold edge connector to interface the proprietary logic to the backplane - so it tells us nothing.
The card itself only contain basic TTL packages (latches, buffers, simple logic gates etc.) so it could do (literally) anything...
I wonder if there is an IC missing - as there is an empty IC socket.
If it was me, I would do a bit of 'wire tracing' from the edge connector (we know what the pinout of this actually is) and see if we can work out the address decoding. A bit of 'reverse wire tracing' from the external connectors next - to see which pins are wired to IC device inputs and outputs.
Dave