One of the earliest instance of either hippopotomonstrosesquipedaliophobia or sesquipedaliophobia in a Google Books search is from Chris Aldrich, The Aldrich Dictionary of Phobias and Other Word Families (2002), which lists both of them, in this entry:

-PHOBIA: FEAR OR DISLIKE OF, OR AVERSION TO ... sesquipedaliophobia long words; also humorously hippopotomonstrosesquipedaliophobia

However, a significantly earlier instance occurs in Dennis Coon, Introduction to Psychology: Exploration and Application, second edition [?] (1980), which includes this footnote:

*Obviously by combining the appropriate root word with the word phobia, any number of unlikely fears can be named. Some are acarophobia, a fear of itching, zemmiphobia, fear of the great mole rat, nictophobia, fear of backing into doorknobs; phobosophobia, fear of fear; and hippopotomonstrosesquipedaliophobia, fear of long words!

But that is as early as the entries get for either word. Two different reference works point out that hippopotomonstrosesquipedaliophobia is one letter longer than supercalifragilisticexpialadocious, a nonce word that became famous from a song in the 1964 film Mary Poppins. It seems likely to me that the hippopotomonstro- prefix attached to the shorter word sesquipedaliophobia is there simply to make the resulting word longer than the Mary Poppins word.

It is difficult to find any mention of hippopotomonstrosesquipedaliophobia that doesn't remark on the irony of the fact that the word for "fear of long words" is such a long word. But it appears to have no claim to existence outside the purposeful lengthening (for effect) of sesquipedaliophobia. Any word that appears on paper is a "real" word, in some sense. But I think it's fair to say that hippopotomonstrosesquipedaliophobia is an artificially long word, not a naturally long one—and therefore that it did not come into existence under the same rules of formation that govern most words in the English language.