Can't restore this one course ... but others are possible.
The course in question is still in legacy files (it restored that way). So that means it started as a 1.9 or earlier .... that's also a factor. One of these days, an update/upgrade to Moodle will announce ... oh, we no longer support Legacy files. So, one piece of advice, even if you can't do it right now ... work on it ... do it soon ... get the course out of legacy. Use a file system repo to link to files ... but don't alias to them! ;)
Reading the history, it could be that the question bank is in need of repair. Besides files, that's the other heavy processing point in backups and restores.
Did you check out the quizzes on the server where I was able to restore it?
7.5M ./questions-DemonChem 1516F-Gen Chem-20160119-2321.xml
On your server, login as admin, then using the URL line, go to:
http://yoursite/admin/tool/health/
It will probably find some errors related to quizzes and provide a 'proposed solution' button/box which is an SQL query one copies and paste into an app that can do MySQL ... uhhhh, command line at the 'mysql>' prompt works also.
Will that fix this course? Well, at this point, I'd say anything would help.
Dunno if you will see anything ... on the server to which I restored, no health check errors ... I expected to see some related to quizzes. On your server, however, you might as it does contain other courses and other banks.
Moosh ... yes, knew about that but hadn't really needed it ... yet. Good to know that Moosh worked with your troubled course.
Do you need the course I restored? I need to remove that which is not used. ;)
'spirit of sharing', Ken