There is no doubt that simple integer ratios between two frequencies produce consonant harmonies. The reverse, however, is not true. If it were, equal temperament would be completely unusable, since, as @badjohn points out, the ratio of every interval in equal temperament (except the unison and its octaves) is an irrational number.
But I'm not so quick to dismiss mathematics as an objective measure of consonance and dissonance. It's just that looking no further than the complexity of an interval's ratio is grossly oversimplifying the phenomenon.
For one thing, the simpler the ratio, the easier it is to hear dissonance when two frequencies are off. Your ear hears sharp or flat unisons more easily than sharp or flat octaves, and, in turn, it hears those more acutely than sharp or flat fifths. Were it not for this fact, equal temperament could just as easily have expanded the octave as narrowed the fifth. (As it happens, the span of 12 fifths is reduced to 7 octaves, not the other way around.)
It's apparent from the graphs in the answer by @topo morto, too. Perhaps it's that we don't hear a minor second as a "simple" 16:15 ratio but as a really, really off 1:1.
That said, slightly off intervals which are very complex but nevertheless approach simple ratios (like a unison) are actually much more interesting to the ear than perfect harmonies. Consider choirs and 12-string guitars, for example. They produce the chorus effect naturally because the constituent sounds are not in perfect harmony. Anyone who's ever messed around with a synthesizer knows that slightly detuning the oscillators creates a richer, more interesting and pleasing sound.
Besides the factors of interval span and timbre, another consideration is the pitches at which intervals are demonstrated. For example, an A7 chord rooted at A1 on a piano sounds awful. The parallel chord two octaves higher is quite nice, despite containing a tritone between the C♯ and the G.
Finally, context also plays into the perception of consonance and dissonance. For me personally, the minor seconds in the Angry Birds theme, while dissonant, are delightfully playful. (The bit with the minor seconds starts around 0:20.) On the other hand, the minor second in your example is torturous. For me, it's clearly the more dissonant interval.