I modified one word to make it work on Auto Grade Essay question(Quiz) (Note: Not just regular essay question).
Download this plugin called "Quiz reports: Download essay submissions"
https://moodle.org/plugins/quiz_downloadsubmissions
you need to change this file called "report.php" under Moodle/mod/quiz/report/downloadsubmissions
Before
line 56, 167, 270 where qtype == 'essay'
After
line 56, 167, 270 where qtype == 'essayautograde'
Result
Download all submission from Auto Grade Essay questions if there is any submission
Feel free to suggest any improvements