The problem seemed to be that a particular folder (the lib/linux-x86_64 folder) contained a file (the DSGReDraw executable) that didn’t have permission to execute as a program. Without that permission, the game fails.
I managed to fix this issue by executing the following command in the root folder (the DreamSaviorGakuenReDraw folder):
chmod -R u+x *
Which gives the current user permission to execute every file in every directory.
So thank you for the recompilation. You might want to include a message on the download screen saying you’ll need to execute this command, though.