The principal way in which this hilarious poem shows the author playing with words is through the creation of the strange and funny names that Adam comes up with as part of his task of naming the animals. Consider some of the names he devises and the way that he shows a love and childlike enjoyment for playing with words:
Thou, paw-paw-paw; thou, glurd; thou, spotted
Glurd; thou, whitestap, lurching through
The high-grown brush; thou, pliant-footed,
Implex; thou, awagabu.
The way that Hollander uses enjambment in particular to focus the humour of his naming also adds humour. Consider the impact of naming a creature "glurd" and then going on to name another creature "spotted glurd." The enjambment serves to act as a kind of anticlimax as we expect something different, only to see that he uses the same name after all.
The poem has a regular rhyme scheme of ABAB, with some half-rhymes used. Rhyme is also part of what Hollander uses to make this poem funny. Note the way that "through" is rhymed with "awagabu" in this stanza, and likewise in the third stanza, my favourite animal name, "McFleery's pomma" is rhymed with "comma." Rhyme is of course no problem when you can invent words that will rhyme with whatever other words you create! All of this focuses on the massive sense of enjoyment that Adam is experiencing as he carries out the task that God gave him. Work can be fun, after all.