The poem is a variable combination of Trochaïc: four pairs of two syllables with stress on the first.
Whén we gráb you bÿ the ánkles,
Then an Iambic tetrameter: four pairs of two syllables with emphasis on the second.
You'll sóon be dóing noble work
Then a final iambic trimeter: three pairs of two syllables with emphasis on the second.
Althóugh you wón't be páid.
The second stanza is not quite the same as the first and takes a few minor liberties. Unlike the first, the second is alternate trochaïc tetrameter and iambic trimeter. The third line is one syllable short. There is a technical term for this. It's called 'catalexis' (which in ancient Greek only means leaving out). So they would call the line an 'iambic tetrameter catalectic' (i.e. and iambic tetrameter leaving out the last syllable!).
I am sure the writer was not thinking in these terms. But the use of trocháic metre tends to be bouncy. Short lines enhances the bounce. The fact each line is more-or-less a self-contained unit of sense rather than flowing on into the next also makes for bounce. Similarly, the shortening of each fourth line gives you a clear metrical ending to each stanza. So the rhythm is highly defined.