The perl regex algorithm/engine is neither DFA nor NFA. The description in Friedl's book is incorrect, and he later have explained that in his website: On the Terms “NFA,” “DFA,” and “Regular Expression”.
In a nutshell, he have used "NFA" to describe regex implementations that have backtracking or backreference, such as /(foo)\1/ matchin "foofoo".
The Perl engine (or almost any other regex implementation out there) cannot be any type of "FA" as it uses backtracking, either recursively or iteratively.
Principle of Least Astonishment: Any language that doesn’t occasionally surprise the novice will pay for it by continually surprising the expert