Fans could be dropping mail off at the theatre (rather than sending it in the mail), and your man would then be delivering it."We've been on the alert for sabotage all through rehearsals, with strict screening of visitors and man-traps outside the stars' dressing rooms; but nary a bite except one poor old stage-door-Johnny delivering fan-mail".
But it would be strange that a stage-door-Johnny comes to deliver mail from other fans, wouldn't it ?
You can speculate, but you asked about the meaning and the answer is that it's not contained in the text you present.It is from "the Exploits of Engelbreht" by Maurice Richardson - a British surrealist text from the 50s.
This particular scene takes place at the "Dogs' Opera"...