The burned thing on the engine is the regulator / rectifier and it was it that failed.
The wire that takes the DC back to recharge the battery is not fused so if it shorts anywhere the alternator just keeps on pumping power down the wire till some thing burns out or blows up or catches fire .
You will probably find the alternator is also deceased .
Use your model numbers 917271121 to locate the parts manual for your mower on line.
In it should be the wiring diagram .