The poem has nothing to do with the word snarky, which means ‘sharply critical’. More precisely, snarky means critical in an annoying, sarcastic, grumpy, wisecracking, or cynical sort of way.
The following analysis of words beginning with "sn-" is from The Guardian (London): "And few groups of words are as useful for verbal snipers, those who sneer, snap and snarl, who resort to the snide, sniffy, snarky, snooty and snotty, as those which begin with an s and an n. That is not to say that all belong exclusively to the world of vituperation. Snug and snuggle are cosy agreeable concepts."
I think this list will come in snhandy one day.