How is this possible?
For a start, they are outstanding musicians, all respectful of each other's roles and of the overall sound. They are well directed - by a leader who gives neat and discreet signals, so that they all know who is taking the breaks and who is to take the next solo and when to go back to Part A. They are seated in such a way that everybody can see the leader's signals (very important). They make sure that all instruments can be heard. Note what discipline and restraint there is among the other players during the tuba solo chorus. Listen to the clarinet and saxophone and note how they never trespass on each other's notes. Importantly, nobody in the band is using amplification, so the overall acoustic effect is fine.