The concept of "dissonance" is actually a broad one.
Strictly speaking, it's just a non-consonant sound, it doesn't mean that it's "bad".
A tritone can be considered dissonant, or even a minor second (or major seventh).
But music is based on time and perception, and it's all based considering the context.
Dissonances create tensions, which demand for a release: the more high and powerful the tension is, the more interesting and satisfying the release can result.
Then there's also the social/historical aspect: some "sounds" that were considered dissonant, are now considered actually consonant. A dominant seventh chord was a basic and important dissonance/tension that required a release at least until ~100 years ago. But you can listen to any standard blues (which uses that chord even for the tonic), and that's not something that requires further release.
To some extent, we can consider dissonances as disturbances, "noise". In fact, even the most basic dissonant sounds create complex and disordered frequencies, not unlike a noise.
In a crescendo-like climax like the one you posted, the intention is clear: more sounds, more dynamics, more tension; hence, more "noise".
Those "distortions" and "wrong notes" played near the end are exactly that: increase the tension, to achieve a better and powerful release.
In fact, you can listen to a similar and interesting effect even at the beginning of that video, where percussive, unpitched sounds (which are fundamentally dissonant) are played before turning to a more consonant section. Even if some pitched sounds are played, they are still dissonances.
Finally, consider that:
- tensions can be achieved in various ways, not only harmonically: consider crescendos (eg.: Ravel's Bolero), or even rests, especially if long or unexpected (the last three bars of Stravinsky's Rite of Spring, or even the passage between the two parts);
- the release part of a tension doesn't mean that the piece has to become "calm", soft and on a basic chord: even the end of a piece can be considered a release (again, Bolero);
- music is, first of all, based on time: even pitch requires time, since it's based on frequency; what creates music is the variations in different time contexts: sound/rest (and amplitude, as in dynamics), pitch/frequency changes;
- everything said above is an extreme oversimplification, as this can easily enter the complex subject of psychoacoustics; but, the point remains, dissonant sounds dramatically help to create tension, and if introduced at a clear climax of a piece, it's not anymore about the consonance of sounds (or, better, its absence), but the effect they create;