He means rhyming as in words ending in the same vowel+final consonants. Japanese syllables are very simple, and typically lack final consonants (except for the nasal phoneme n/m).
There are two aspects to meter; the placement of stressed syllables and the placement of syllables of different lengths itself. Actually English as opposed to Greek and Romance languages that are not French has stress patterns that are highly dependent on the phrase rather than on syllable position in words, and so traditional forms are felt to be quite artificial in English, and perhaps this encouraged the development of free meter in modern English poetry.
Anyway, the stress aspect of meter I don't think features greatly in Japanese poetry. On the other hand, meter still features prominently in Japanese standard poetic forms; are characterized as having a set number of syllables in each line, but renku looks instead at the number of morae (short syllables have one; long have two).
I'm sorry, I didn't intend to make a case for Japanese not rhyming with what I mentioned. I intended to illustrate how rhyming looks like in Japanese, but rereading my comment it does indeed look like that.
I just wanted to establish that Japanese poems were characterized primarily by # of syllables or # of morae, and were quite free in their distribution of stressed syllables or long/short (heavy/light) syllables, as opposed to most European forms.
I'd also like to address a misconception of the original comment I was responding to that rhyming in poetry is prevalent in a language because it takes skill. It's primarily a matter of poetic tradition whether a language's poetry cares about rhyme. As darkwater's comment points out, Italian has plenty of rhymes and its poetic forms use rhyming extensively.
There are two aspects to meter; the placement of stressed syllables and the placement of syllables of different lengths itself. Actually English as opposed to Greek and Romance languages that are not French has stress patterns that are highly dependent on the phrase rather than on syllable position in words, and so traditional forms are felt to be quite artificial in English, and perhaps this encouraged the development of free meter in modern English poetry.
Anyway, the stress aspect of meter I don't think features greatly in Japanese poetry. On the other hand, meter still features prominently in Japanese standard poetic forms; are characterized as having a set number of syllables in each line, but renku looks instead at the number of morae (short syllables have one; long have two).