Looks to me like the "Both" and "2" connections are swapped.
One thought though: the function of the terminals on the back may NOT match the operator labels on the front. Are these lables what you have read on the back side where the wires attach, or just where they enter the switch when viewed from the front?
One reason I ask is that I would not expect the wire terminal to be labled "BOTH", I would expect it to be labled "Com" or "Load" or "out".
There is an easy way to tell: With the engine off, Switch to "1". If it is wired wrong, then you won't have any electrical power to the starter. If you can start the boat with the switch in "1" , "BOTH" and "2" but not in "OFF" then it is probably wired properly.