From everything I’ve read my understanding is that there is no way for the site to work without also having the MySQL database files, which I don’t think are in that download.
Correct on both counts.
Without the database, the site cannot be re-created.
There are no database "files" per se. The site database would have been in her previous hosting account's database server. Unless an export file was created and downloaded from it, and she no longer has access to the hosting account, you are out of luck.
The only recourse I can think of is to contact the previous hosting provider to see if they can either reset her credentials so that she can log in and do the db export, or if they could do it for her.
