Here is a link with scans of a legit cart of Fatal Fury 2 for you to compare (its easier for you since you have it on hand)
From what I can see I think that someone has tined the contacts using solder, a soldering iron and solder wick. This is a method when the contacts are very corroded or damaged somehow. This isn't bad. I have done it on other retro computer expansion slots myself.
So, the cart has been definitely opened in the past by someone else. Was it sold to you as "working" or "untested" ?
The contacts don't lose their gold copper color on their own.
The best way to clean dirty contacts since you have the cart open and have very good access to them, is to rub them with a pencil rubber (the white one prefferably since its softer, or the orange one)
5 x Staedtler Mars Plastic Pencil Eraser Rubbers School Office Drawing: Amazon.co.uk: Office Products
After you clean them as much as you can, them rub the contacts with alcohol.
If that doesn't help then it's probably a bad cart.
Also check for anything suspicious on the other side of the boards. Do the boards look like they have been tampered with (besides the contacts)