I think the phonics method teaches people to recognize the sounds of letters, syllables and words. After that, we begin to memorize the whole words that we learned syllable by syllable.
But any explanation of how someone begins to learn starting with the whole word just sounds like nonsense, or some cumbersome memorization procedure.
For the most part everybody is unaware that the MACULA (as it's called these days) has nerve tendrils going from the left side of the center of the eye to the right side of the visual center, and those from the right side of the center of the eye to the left side of the visual center.
There they match up with other tendrils from the other eye. As your eye traces through printed words it sees both the leftside of the word and the rightside of the word SIMULTANEOUSLY and the brain scans the other letters or hieroglyphic elements in between and matches them up with something meaningful in its vast warehouse of word parts lists.
This has to work with alphabets, syllabaries, pictoglyphs and hieroglyphs. There may well be other writing systems somewhere that this would accommodate.
Then there's the classic question ~ why is it an educated person knows how to read so many tens of thousands of words he's never heard? He certainly doesn't need the phonemes (syllables or character marks) in mind if he's never heard the word!
BTW, the theory discussed in the paper I referenced would also explain why Chinese have a gene that facilitates their accessing TONES separately from the words. When it comes to Chinese-like languages you need an additional sound pathway to pick up on the word you are dealing with ~ hearing the syllables just doesn't do the trick.
The Chinese also have a universally taught written language that has no "sound values" at all ~ it's strictly visual. Think about that a moment ~ spoken Chinese uses syllables and tones (spread across the width of the syllable) yet written Chinese is 100% look-see-think!