After Kayden obtained the Ghost Fire Sapphire, he didn't stop looting the Hidden Treasury of Windesburg Hotel.
However, he didn't find any other game items in the Hidden Treasury aside from two more Ghost Fire Sapphire. In other words, there were three Ghost Fire Sapphire in total.
Kayden handed one of them each to Shirohige, Kuroneko, and ProGamerXD. After all, those three didn't have any game items.
On the other hand, Kayden handed the Red Purification Pill to Kodokuna Kenshi.
After all, if they complete the first main objective, they'd probably only be able to bring one game item to the real world.
Since Kayden and the other authority users in their group will bring the authority to the real world, those who didn't have any authorities will be in charge of bringing the game items to the real world.