Fixable but may take a bit of time. You may need to go a little higher in parts replacing. For example - R45 has corrosion as well.
Hard to tell if there is corrosion under items such as Z1 or the DIP switch without pulling them.

Start with a good cleaning and go from there. Make sure to clean off any alkali that crept under the solder mask - particularly near Z1 and Z2 (you may need to replace both depending on what it looks like under Z1).
But remember - those DIP switches don't like water. Even if they are "dried" or blown out - there is always a bit of moisture left over in them. Over time, they develop a nice blue-green layer of corrosion and stop working.

Somebody replaced U6 (without installing a socket). Looks like they may have damaged thru-holes resulting in the three extra wires.

U13 has also been replaced. The repair person didn't clean up the flux resulting in what looks to be a heated spot on the bottom of the board. Clean that up with alcohol and it'll look just like the other joints.

See here for more info:
https://www.pinwiki.com/wiki/index.php?title=Gottlieb_System_80#Battery_Leakage_and_Corrosion

Yep, that's what happens when you flip a board and see the mirror image - your eyeballs follow the traces to the wrong place...
They changed the ROMs resulting in the wiring changes.

The J1 connector seems to only have a corner missing on the 2nd pin. The plug contact on that pin may be reaching in far enough to still hit the remaining pad. Unless the copper is lifting from the board, it seems to mainly need a good cleaning and re-tinning. To do a complete repair, you need copper tape and practice. not sure you need to go to that extreme yet.

But at this point, I think it's too soon to go with the replacement board method.

There's a couple vids on youtube for this -- such as this one: