Complex sentence: Haidy's name was not included on the Cup because he was not a regular member of the Red Wings but he did qualified to be on the cup, and so the NHL credits him with winning one Stanley Cup.
Split into simpler sentences: Haidy's name was not included on the Stanley Cup, because he was not a regular member of the Red Wings. He did qualified to be on the cup, and so the NHL credits him with winning one Stanley Cup.