It's wired correctly, although that lamp cord needs to go.

It doesn't really matter which switch leaf each wire goes to, as long as one comes from the center solder tab, which has both large and smaller gauge wire, and from the tab with the smaller wire. That tab carries the current that comes from the flipper button switch. That is the hold side. It is shorted out when the EOS switch is closed. When the switch opens, the hold side is now in series with the power side, which is the side with the larger wire and which gets power directly from the solenoid power wire.

That is your "Hot" side of your power from the transformer that has been daisy chained together. This would be on the Coil side of the schematic. (Black-hot, White-Neutral, Green Ground).

The Right side as two wire allowing the the power to flow to the next coil. The left has one because it is the last coil in the series. (like when you have several wall plugs on the same breaker).