This song --to me---showed no humour or satire.

Humour-no, Satire-yes.You are right;there isn't any true humour in the song,though most listeners laugh at the lyrics.Why?Because,in my opinion, this shows a growing insensitivity to violent acts in modern times.Perhaps this is, in an ingenious way, what Brodsky is pointing out in his song.
Satire I see in the song.The singer is a caricature of the idiots who succumb to road rage and do violent things.Never would I attribute these characteristics to Bruce Brodsky.