"Loot itself is a Treasure costing $5 or more, so a player gaining one will trigger Cutthroats."
I assume the implication of "Loot itself" is the Loot gained by triggering a Cutthroat. But is this actually possible? If someone gains a Gold, my Cutthroat triggers, gaining me a Loot. But all Cutthroats already triggered from the Gold gain, so how can my Loot gain trigger any Cutthroats?
Thinking about it, I think the only way is if someone played a Cutthroat from gaining the Gold or the Loot, before I gained my Loot. Let's say my left-hand player gained a Loot from their Cutthroat, reacted with a Sheepdog using Way of the Mouse playing Vassal, and Vassal hitting Cutthroat. Then I gain my Loot, triggering their new Cuttroat. So I guess we need Way of the Mouse and Vassal?
EDIT: No, also if the player gaining the Gold (the player in turn, let's say) gained Cutthroat from Haggler or Architects' Guild, they could play it with Innovation or similar.