If you miss out the vowels (like Hebrew) the first sentence of Harry Potter and The Philosopher's Stone has exactly 64 letters.
Because I had nothing better to do this evening, I put those 64 letters into the square the OP suggested.
There are plenty of words one can make running horizontally and vertically, adding in vowels where necessary. Some of them even relate to Harry Potter for example Ron, auror, seer, late, shoot, fire, Lord, fatal, keeper...
However, there is no suggestion that JK Rowling was trying to encode anything into her work, simply that given a few letters the mind will find patterns. Ascribing meaning to those patterns is where you are making a mistake, Kingfisher. Just like the Bible Code, this is no more than an artefact of a few letters being able to be combined in many thousands of ways to form words.