Simply put, the Zoo of Death is a symbol for all of the insecurities that Prince Humperdinck feels as a man. Deep down, the guy is a total coward. So what better way to convince himself he's not a coward than to stock a zoo with all the deadliest animals in the world and spend his days hunting and killing them? The Zoo "was kept brimming with things that he could hunt, and it really wasn't like any other animal sanctuary anywhere"(2.9). Perhaps it's unlike any other animal sanctuary because, um, animal sanctuaries are places where animals go to be protected.
The Zoo isn't so much a zoo as it is a death trap that no one but Humperdinck should be able to survive in. Each floor features more terrifying animals than the one before it, and it's easy to envision Humperdinck growing more and more pleased with himself—his chest puffing out with pride—as he makes his way through this rigged game of terror.
It goes without saying that Humperdinck likes to feel challenged. That's why he always keeps the fifth and final level of the Z.O.D. empty, so that one day he can fill it with a beast that's truly worthy of him:
The Prince constructed it in the hopes of someday finding something worthy, something as dangerous and fierce and powerful as he was. (2.12)
Does he put a lion in there? A giant? Nope—he puts Westley in there. And while Westley may be the greatest adversary Humperdinck has ever faced, he doesn't wind up doing very much facing of Westley one he captures him. Instead he basically just leaves Westley to be tortured by Count Rugen's machine.
Sure, Humperdinck turns the machine up to full blast, but that Westley—supposedly someone "as dangerous and fierce and powerful" as Humperdinck—is already tied up says a whole lot. This isn't a fight that Humperdinck wins; it's a guaranteed victory for him. In being such, it reinforces the Zoo as a symbol for his cowardice and insecurity. Humperdinck isn't brave enough to risk losing, or confident enough in his own ability to actually win against the man he identifies as his most worthy opponent. It's pretty weak on Humperdinck's part.