Sounds counterintuitive. I'm pretty sure this is a 9V boombox. With a 9V motor, it seems like a zener diode would be totally unnecessary unless to account for AC power which could run over 9V. Still, that's generally not how zener's are installed in a circuit to regulate voltage, it would typically be installed in conjunction with a transistor and resistor to make up a voltage regulator. Personally, I've never seen a zener diode installed directly on a motor. On the other hand, flyback diodes are common. They run across the motor leads (like yours/those) and the purpose is to provide a return path when a circuit is switched off, which with inductive loads (like motors) can result in voltage spikes. This is because inductors store energy that will insist on going somewhere when the circuit is switched off, and the magnetic field collapses. However cassette motors are so small that I really don't think a flyback diode is necessary as the inductive load is not that great. In either case, whether with a zener diode intended to regulate the voltage, or as a flyback diode, the cathode would be installed at the (+) end. If that really is a diode and if the cathode was installed at the (-) end, I believe current would flow through the diode instead of the motor, and it would likely just blow up or if the diode was robust enough, the motor would never spin because all the current goes through the diode.
What exactly is the problem beside the obvious broken component? Does the motor not spin? Because if it doesn't, replacing that diode isn't going to get it going again. In fact, if that is a diode, the motor should still work fine without it. 95% of all boombox motors don't have one, and the other 5%, I can't recall those, though admittedly my memory is poor these days. If your motor is not spinning, I'm sure you can replace it with a standard 9v motor, as that clearly looks like an internally regulated motor and not one of those 4 or 6 wire jobs that are specialized.
As for the service manual not showing the diode or the capacitor, that's not unusual. That motor is intended to be replaced as an assembly, which includes the circuitry attached directly to it. So the motor "assembly" will show up in the manual as just the motor. Internal to that motor is speed control circuitry too and you'll notice that those also do not show up in a service manual as those were never intended to be serviced separately.
