David Appleyard's Guide to Article Usage in English gives a possible answer.
An article is unnecessary in official job titles if there is only one person holding this position at any given time.
Paul Fischer is the only author of his work. So, it's unnecessary to put an article in front of "author".
Let's take a look at the original text of Copyright, Designs and Patents Act 1988:
Right to be identified as author or director.
The author of a copyright literary, dramatic, musical or artistic
work, and the director of a copyright film, has the right to be
identified as the author or director of the work in the circumstances
mentioned in this section; but the right is not infringed unless it
has been asserted in accordance with section 78.
They use both of the adaptations, the one with article and the one without article, in their text. You could think of this as a way of telling the reader that he is allowed to use both of them.
Another possible explanation could be that authors refer to their "Right to be identified as author or director", because a "Right to be identified as the author or director" does not exist, since the corresponding section 77 does not include the article "the" in its title.