Is there something wrong with it or do you just feel it is incorrect?
Looks good to me as long as you have ground and one or two 30v wires going to the kicker coil, which it's hard to tell, but it seems you do. If so, your wiring looks fine. That switch is there to detect when the ball is in the outhole. Looks a lot cleaner than a lot of things I have seen.
I would leave it be and if you're experiencing a problem, it's likely not there. All the wiring is original besides those extension wires which were replaced or the original wires were cut way too short. I don't think it looks very amateur, not original yes, but I mean there's not many better solution for what they were trying to do besides shrink tubing and soldering the extension wires to the old wires - those metal "bridges" almost look original but that is unlikely.
Looks to me like a "fix" and not a hack. Not many ways to make it better. If it's working, leave it be and enjoy the game IMO. If not, it doesn't appear to be a problem so I would bet it lies elsewhere.