Why is this funny? Simply because there is a shift in the frame of reference. Postmen/mailmen deliver mail. That's their job. So when he says what he says here, he is shifting to another frame of reference: now he is a curmudgeon who's only concerned with his own comfort, not with doing the job he's paid to do.
This is the stuff of humour, but it is also the stuff of social dysfunction. Watch out for it, watch out for the many occasions when the social order is disrupted because someone doesn't play the game according to the rules any more. Sometimes it's funny, but in the long run, it's bad for social cohesion.
It's a good joke, though, isn't it?!