Whoo nostalgia time. The MC6821 is an I/O chip, with 16 I/O if I remember correctly. The whole of that board is what we had to do before micro controllers. The chip with the label on is the EEPROM that held the code, the 24 pin chip is a serial interface, and their should be a MC6802, or MC6800 in their as well.
If you are replacing just that board then you should be able to wire those connections to the MC6821 directly to the Arduino or port expander connected to the Arduino. That means you can use the existing bulb drivers as the brown boards will be the bulb drivers. Same goes for the input switches, if it goes to a MC6821 it can be wired directly.
will have to check the 7segment displays tho.
Again you would not power the display from the Arduino but use the drivers that the MC6821 talks to. It is just a matter of tracing the wires.