Dies Irae might well be, and often is, the title of a piece of music. You might write "Mozart's Dies Irae" and use italics to indicate the title. However here "Dies Irae" is not being used as a title - it is being used to refer to a particular kind of musical composition. Talking about "a 'Dies Irae'" indicates this. As such it wouldn't deserve italics. Almost invariably those pieces have the title Dies Irae, so italics might be justified - however again, having used italics specifically for a title elsewhere, the author might decide using them here might be confusing. The author might still want to separate the 'Dies Irae' from the rest of the text, so quotes is justifiable.