The point is that if they really were logographs, and not just a complicated syllabary, you would get a lot more than the equivalent of two or three letters out of them.
The Chinese (Traditional) translation consists of 2202 characters (UTF-32). The English translation consists of 8555 characters. This amounts to ~3.88 English letters per Chinese character, quite a bit more than "two or three".
None of the actual syllabaries get even close to the density of Chinese. Korean, the closest comparison point (a true syllabary) clocks in at 3856 characters - a far cry from 2202.
You are arguing with something that the article did not say. The substring "logo" does not occur in the article. The article makes no claim about what the Han script encodes beyond implying that the Han script isn't alphabetic, which shouldn't be controversial.
