The claim is technical, so if you don't understand phonological theory and you don't understand Professor Hyman's "stuffy paper", you probably won't understand my stuffy explanation.
The underlying question is, what are the universally mandatory representational objects of human languages, and the related question is what are the optional objects. Example: it turns out that all languages have vowels and consonants, so you could say that vowels and consonants are mandatory. Some languages have ejectives and others do not: ejectives are optional. Every language potentially could have ejectives, or implosives, but some don't have them. Phonology has used two distinct systems of logic for building the theory: "If it's possible to say that X is present in all languages, you must say it is present in all languages", and "Only say that X is present in a language if there is direct evidence for it in the language".
The notion of syllable is one of the notorious examples of things that have been arbitrarily claimed to exist in all languages (similarly, "noun" and "verb" are stipulated universals). The stuffy argument is that there is no sufficient evidence to support the claim in Gokana that there must be syllables in Gokana. There is a pretty long literature regarding syllables and alternatives to syllables, the point being that there may be evidence for other things that aren't really syllables. For example, a cluster of prevocalic consonants might behave like a single unit, but we could say that "they are in the same syllable" or we can set that "they are in an onset". Hyman in his original paper points out, correctly, that reference to "mora" is sufficient. It is not seriously disputed in the theory that the concept "mora" is necessary; it is seriously disputed whether an additional concept "syllable" is sufficiently motivated. But of course, the question of something being "sufficiently motivated" depends on your logical framework: the earlier epistemology of the field was heavily tilted towards arbitrary claims as to what is in Universal Grammar, and it is really only recently that the approach changed towards a more minimalist version of UG.
It's not clear to me whether this is the part that you didn't understand: I'd say that reading Hyman's original descriptive works (1983, 1985) is the first thing you should do to understand the language facts.