What Haik-Vantoura did was nothing like "The Bible Code" and other various numerologies. I think you're getting hung up on the opening sentences in the video, which, in my view, puts forth an erroneous presupposition as fact. The Hebrew Scriptures were not written as songs, though they contain many.
But that they were all put to music in the schools and the synagogues, there is no question.
The point here is not looking for a code in the Hebrew text itself, but deciphering the Taamim, or 'accent marks' as they're called by some, symbols of undefined meaning above and below the standard Hebrew text .
The ancient names of the accent marks are musical, and their shapes can be easily duplicated in chironomy, musical direction with hand signals. And the Hebrew name, Teamim, can by amplification mean tune or melody.
Haik-Vantoura was a learned Jewess, and also a musicologist, not a mere a musician. I have the English translation of her book on my shelves, and in it she makes a good and sholarly case for her theories, and she had gained the admiration and caught the attention of some none-too-marginal rabbis. But, without a high degree of musical expertise, one would find the application of her music theory difficult to follow.
To me, the fact that her key, being consistently applied to the symbols (not to the text) in the order as they appear in the standard Hebrew text without having to add or take away even one, yields these very natural sounding melodies is the best evidence by far that she is on to something. This certainly couldn't have been duplicated by any kind of creative math.
I said all that just to say, this is nothing like the Bible Code or numerology or finding the Beast of Revelation in a purple dinosaur or other such superstitious freakdom. It's just musicology.