I have no Hungarian, but here's a gesture toward an answer. Quantitative meters depend on the patterning of short and long syllables. They are thus different from accentual-syllabic meters, which depend on the patterning of stressed and unstressed syllables. Accentual-syllabic prosody has been discussed on this forum in a few answers; the last linked one goes into some detail about how meter works in English poetry. To native English speakers, having stress patterns vary over speech or a line of poetry seems so natural, that it's hard to wrap our minds around the fact that other languages have a different measure of rhythm, one that counts syllable length rather than accent.
I can't possibly come up with a better illustration of the distinction between stress and length than the one given by @user14111 in the comments to this question, so Imma shamelessly steal it and put it right here:
the Hungarian word kovács (= smith) is a trochee in stress versification, since (like every word in Hungarian) it is stressed on the first syllable; but it's an iamb in quantitative versification, since the o is short but the á is long, as shown by the accent mark.
Let's unpack this by looking at three different meanings of accent and two of length. Sorry, these things are complicated.
- A distinctive way of talking, where speech patterns reveal the speaker's geographic or class origins: a Southern accent, an Indian accent, a Cockney accent.
- A diacritic, which is how user14111 uses the term when he speaks of the accent mark over the á. In English, we tend to say "accent mark" rather than simply "accent", but the latter isn't uncommon. For example, a teacher of French might say to English-speaking students that because sûr and sur are different words, as are ou and où, it's a spelling error to leave off the accents.
- A verbal stress, marked by speaking the stressed or accented syllable somewhat louder and/or longer than the syllables surrounding it: in the word trepidation, the accent falls on the -da, the penultimate syllable. This third is the relevant meaning of accent when it comes to accentual-syllabic prosody.
Next, syllable length.
- The first meaning is simply a matter of timing: for how long one maintains a vowel. English speakers can readily hear and maintain a distinction between long and short syllables in this sense, e.g., between a short 'u' (as in foot) and a long 'oo' (as in boot). But how long one holds a syllable doesn't actually matter for accentual-syllabic versification. I put my feet in boots that fit is a regular iambic line in English despite the fact that two of the accents are on short syllables and two on long ones. Syllable length in this sense simply doesn't matter for versification in English.
- Oddly enough, length in that first sense isn't fully determinative for versification in quantitative poetry either. It's a second meaning of length that matters for quantitative meters. Here, length is an abstract measure of a syllable. A syllable is given one of two possible weights, and is described as long or short depending on that weight. Sometimes, as in Prosodic Weight: Categories and Continua by Kevin Ryan (which you cite in your question), these categories are called heavy and light. These terms are more accurate, but in my experience less commonly used, than long or short for designating syllable weight in quantitative meters. Where in English, metrical feet like iambs and trochees are defined by the patterning of stressed and unstressed syllables, in languages that use quantitative meters, such feet are defined by the patterning of weighted (heavy or long) and unweighted (light or short) syllables.
So the critical question is, what are long and short syllables in the context of quantitative meters? The answer is: those syllable weights are conventionally determined by certain well-specified rules that are related to, but not exclusively determined by, whether the vowel within the syllable is temporally short or long. To take an example: in Sanskrit, a syllable that has a temporally short vowel is by default metrically short too. But in certain cases, it is considered metrically long. One such case is when the vowel precedes a consonant cluster. Let's assume for the moment that kit and kilt are Sanskrit words. In both, the i is a temporally short vowel. Kit would be a metrically short syllable as well. But kilt would be considered a metrically long syllable, because -t is a single consonant whereas -lt is a consonant cluster.
This disconnect between temporal and metrical length might seem confusing, but think of it as a metrical equivalent to grammatical gender. There is no natural or logical reason that a leg (la jambe) is treated as feminine and an arm (le bras) as masculine. It's just a convention of the French language. Likewise, there's no natural or logical reason that of two syllables with the same i vowel, one would be considered metrically short, the other metrically long. It's just a convention of Sanskrit prosody.
The point is, when we speak of syllable length with quantitative meters, we mean syllable weight as defined by metrical rules. Those rules are related to, but not coextensive with, vowel length. They are specified with regard to the interaction of vowels and consonants. And of course of vowels with vowels: diphthongs, like consonant clusters, are considered metrically long in Sanskrit, and I'd guess in other languages that use quantitative meters as well.
And those metrical rules are language-specific. Spanish, too, uses accentual-syllabic prosody, in that both the stresses and the syllable counts matter; but trying to apply the rules of English prosody to Spanish poetry, or vice-versa, would be ludicrous. So while Greek, Latin, Sanskrit, and (I gather) Hungarian all use quantitative prosody, without actually knowing Hungarian, I can't answer this question, as I've just proved at excessive, er, length. Hence, as I said earlier, I'm merely gesturing / gesticulating / hand-waving. But in order not to be entirely useless, here is a translation of bits and pieces from the Hungarian Wikipedia page on Időmértékes verselés:
Temporal poetry in literature is a form of poetry based on the alternation of short and long syllables. ... Hungarian is one of the few modern languages that is by its very nature suitable for temporal verse (since Hungarian already distinguishes between long and short vowels). So temporal verse has been written by many poets from János Sylvester to Berzsenyi to Radnóti. ... In Hungarian literature, time-observing poetry appears in the 16th century (through János Sylvester), but it was only at the turn of the 19th century that generally accepted rules were formed, as a result of the debate of the so-called classical Triad (Dávid Baróti Szabó, József Rájnis, Miklós Révai)—the prosodic debate.
Alas, aside from these generalities, the specifics of the discussion are lost on me. Let us hope for an actually qualified person to provide a real answer soon.