It's true that in Classical Latin, ille is a demonstrative pronoun (corresponding to that), not an article; indeed, articles as we know them in English do not exist in Classical Latin. However, that's not the entire story.
Ille in Classical Latin
The meaning of ille in Classical Latin is not so narrow as to exclude its use in these book titles. Allen and Greenough describe the "honorific" ille as follows:
It is sometimes used [...] (usually following its noun) of what is famous or well-known1
Similarly, Gildersleeves includes the following usage:
That which is well known, notorious (often put after the substantive): tēstula illa, that (notorious) potsherd [...] illud Solōnis, that (famous saying) of Solon's.2
So we can see that even in classical Latin, using ille in these book titles can indicate the notoriety of the Pooh and the Hobbit in question. This is similar to the sense in English of saying "Not just any hobbit, but that hobbit" to identify a well-known one.
Ille in Late Latin
Following the Classical period, ille quickly began to be used more distinctly as a definite article, more like the in English. One of the earliest examples of this appears in the Peregrinatio:
But already in the fourth century, the author of the Pilgrimage to Holy Places had begun to employ ille as a definite article: toti illi montes, she wrote, meaning "all the mountains," not, as would have been the case with a writer of Classical Latin, "all those mountains."3
By the 6th century, this usage was apparently common: Gregory of Tours used ille as a definite article "almost as freely" as the articles in modern Romance languages are used.4 An 8th-century example of this is Hygeburg's Vita sancti Willibaldi.5
Pooh and Hobbit
The use of ille in these book titles can be defended in Classical Latin as emphasizing how well-known the protagonists are. And if that justification is for whatever reason unsatisfactory,6 we can appeal to the usage of ille as a definite article in Late Latin.
References and notes:
- New Latin Grammar, page 178, §297
- Latin Grammar, page 193, §307
- Joseph Solodow, Latin Alive, page 239. See also the following citation for more on this work.
- Edward Bechtel, "Sanctae Silviae Peregrinatio" in Studies in Classical Philology, Volume 4, page 144
- James Clackson, A Companion to the Latin Language
- I've seen it argued that the ille in Hobbitus Ille unduly emphasizes the importance of Bilbo, given Tolkien's pains to portray him as a typical hobbit. I'm not convinced (surely Bilbo turns out to be a very atypical hobbit), but even admitting this argument, the author of Hobbitus Ille, to put it generously, does not appear to have attempted to translate into high Classical Latin. Instead he adopts a more accessible style that borrows some aspects of Late Latin, and on that basis ille in the title could be defended.