First, the Insignia of the Clocktower represented the Clock Tower Gang, known for creating time-related artifacts. The card Daniel wanted, "Clockwork Enclosure," was one of their inventions according to the lore.
Second, the Insignia of the Beast was the symbol of the Beastmaster Conclave, specializing in raising and taming magical beasts. They even used various methods to extract beast parts without killing the creatures.
Third, the gold coin insignia with a lion head represented the Association of Prosperity, the gang that controlled economics and wealth in the "Rule of the Backstreet" lore.
Daniel remembered that this card game was set in an alternate world where magic and mystic arts were well-known facts. There were no countries, only territories controlled by gangs, each with different policies.