You should only remove the gear that has the rubber o-ring on it and the small gears that bridge that to the main sprockets. Keep the 2 sprockets and the gear between them. Most cassette players have a part that checks to see if the 2nd sprocket is turning. In a normal cassette the 2nd sprocket turns thanks to the 1st sprocket pulling on the tape which is wound around the 2nd. In these adapter that happens by the 1st sprocket turning the middle gear which turns the 2nd.

2 unanswered questions: 1st, is the power supply designed to work anywhere in the world with Apple only needing to plugin a different power cable before they ship it off? 2nd, what is the make/model of the tweeter or did Apple make their own?