What kind of wordplay is this?
Trapeze itself is a kind of (vague or complex) onomatopoeia. The word swings and lingers, as you say it. The word is also phenomime, or shape word, at least on some highly abstract level with "e-z-e" — emulating the visual akimbo of a body on a trapeZe. Or the two e's being the open space and the Z the body within it.
The ape enters the equation, which intensifies the onomatopoeia/phenomime. Because it feels natural. It fits so well.
(Answer: Analogous Intensifier of an onomatopoeia? Haha.)