I think it's you that has missed the point. Syllables have a very loose correlation to information. So great; we can stream out 39bits worth of syllables / second. In what way does that describe how information dense those syllables are? Context matters here.
Jokes aside, I agree that estimating the average absolute information content of a syllable seems pretty absurd.
However, if the primary goal here was to determine whether some languages convey more information per unit time than other languages, I think the authors did fine. To this end, they needn't define information per syllable in anything other than p.d.u. - procedurally defined units. If average Vietnamese speech has 2x the number of syllables/min as German, but it takes the same amount of time to recite War and Peace in both Vietnamese and German, it suggests that both languages convey the same high-level information 'per unit time', but not 'per syllable'.
And basically that's all they did... "We computed the ratio between the number of syllables [in the text passage] and the duration [it took to recite the passage]"
And yes, I know information theory. It's language that these folks - many of them prominent and celebrated within their utterly normalized professions, just like in the days of phrenology - are fundamentally mistaken about. What quantity of information do you think there is in the word "trump," for instance? Is it the same over time, to bring up just one feature of how this funny thing called context informs human speech?
Wittgenstein's Philosophical Investigations is a good place to start if anyone's interested in understanding this issue.