What Zarlino (or, more specifically, the Greeks) is talking about is proportions of small integers. The octave, for example, has a ratio of 2:1; the fifth 3:2. Zarlino is arguing that since the fourth has a ratio of 4:3, it, too, like the fifth and octave, should be considered a consonance.
So even though other intervals are "rational" in the modern mathematical sense, the concern for Zarlino (i.e., the Greeks) was ratios of small integers.