The Nairobi Trio was a skit Ernie Kovacs performed several times for his shows. It combined many existing concepts and visuals in a new and novel way.
People in gorilla suits was already a comedy staple. Well known or predictable music pieces gone awry is still funny, whether Stan Freberg, Spike Jones or P. D. Q. Bach. The "slow burn" of one character annoying another resulting in eventual retaliation was not new. But the combination of all those ingredients was amazing. It was allegedly inspired by a children's animatronic music box: the three gorillas are robots playing the instruments but when one uses the other's head and hat as a drum, the conflict begins. But being robots, they're all slow and limited in action (Shields and Yarnell did similar skits) which clearly plays on the viewer's anticipation of the conclusion.
Jack Lemmon is known to have performed in the skit.