So if Death was a real entity, and his job was to collect people's souls and send them to the netherworld, and he was thus obviously very busy, don't you think that he would have put up more of an argument to Antonius Block gaining a reprieve by virtue of a chess challenge? Basic conversation (I'm changing like 4 words here):
Death: I'm going to kill you.
Antonius: Can't you wait like 2 days?
Death: I'm too busy.
Antonius: I bet I'm better than you at chess.
Death: Okay, let's play 2 day long game of chess and if you win you live and if I win I get to do my job, which I'm expected to do even though I'm not paid.
Does Death have low self-esteem or something? It's like arguing with a blond.