Is the contact worn down to the Bakelite? I don't have much experience with this type of repair, but if I had to guess, solder would probably be too soft to be a long term repair. It might work for a while, but the little snow-shoe connector will probably dig the rut out again in short order.
If it's not worn down all the way through the metal, I'd just pull it apart, clean the grime out with a degreaser, and maybe lightly abrade the metal with a green scotch brite pad (something that won't take any more metal off, but would get some corrosion off).
Before reassembling, lightly grease the face of the stepper with teflon grease--that'll keep the metal from wearing out more, and the teflon will keep dirt from sticking. If the game is in a home environment, you'd be hard pressed to wear it down moreso.
Good luck.