Well, it isn't a reference to Kaitou Kid. It is a reference — both of them are — to the broader phantom thief genre, which goes back in Japan to the Fiend With 20 Faces/Man of 20 Masks (created by Edogawa Ranpo in the 1930s, and reused by many since), and his predecessors in English and French mystery fiction like Raffles the Amateur Cracksman and Arsène Lupin (around the turn of the 20th century). There's dozens of phantom thieves in anime and manga, and they all use a lot of the same tropes; both Kaitou Kid and the Phantom Thief Eli card set are very consciously playing in that field.
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