Isn't an alphabet an "alphabet of signs"? The way I heard it in grad school is that each of the signs in a syllabary represents a syllable, rather than an individual sound, as in an alphabet. I believe Japanese has a syllabary.
You are correct. :’) This was the writer’s way of explaining it without going into a bogging-down detail. Alphabets caught on because they are easier to learn and easier to teach, and more useful in other ways. Syllabaries are way older though. Once people were used to writing systems of that kind, they usually produced easier ways to write, based on the older, underlying system, while simultaneously continuing to use the older system for recordkeeping, official business, diplomatic communiques, and religious uses. The Rosetta Stone has the same proclamation in hieroglyphic, demotic, and Greek, for example.
The Korean system shows you where to put your tongue in your mouth when you pronounce the various syllables. It's missing a few sounds which limits its ability to communicate Indo-European languages.
Japanese has THREE writing systems ~ http://www.cjvlang.com/Writing/writjpn.html gives a fair description.
Syllabary's are NOT alphabets. Their proponents claim them to be easier to learn ~ which is probably true.
Ideographs require substantial additional education to be able to use them ~ my understanding is that to become adept at written Chinese you need about 8 years of study. American Indian sign language ~ possibly a derivative of the earliest sign languages used in China, is fairly easy to learn if you can remember right and left.