If you can't find an alternator on the engine, then there are likely permanent magnets fixed to the flywheel, and a stationary coil near the flywheel, that is energized when the flywheel spins. Its actually a type of alternator.

Most rider engines have an alternator located under the flywheel. The alternator consists of magnets and a coil of wires. The ignition system magnets are not part of the alternator.

Here are some thoughts on the dead battery.
If the engine was stalled and the ignition/starter switch was left in the on position, there may have been an electrical draw from the afterfire solenoid. Your ignition switch may have been turned to the headlight position after the engine was stopped.