Actually, the way I interpret it is: all demons feed on suffering, and all of them have different ways of going about it. Evelynn takes the most direct route by seducing people and then killing them as slowly as possible. Nocturne tortures people by giving them prolonged nightmares that most of them never wake from. Tahm Kench doesn't even really feed off of 'greed,' so much as the anguish it can bring. He gives people what they want, only to watch as they lose all of it. The guy in his reveal trailer got a whole new life in a foreign land and even married a princess, but had to watch as Tahm took it all away. The guy in that audio drama got so addicted to gambling that he repeatedly threw away all of his money because Tahm planted the idea of "going for even bigger wins" into his head.
Demons in League don't inherently feed on emotions, but rather, the suffering that emotions can bring: lust, fear, greed... All of them are tools that the Evelynn, Nocturne, and Tahm Kench use to exploit humans and put them through as much agony as they can.
