Honestly I respect his decision even if it was 100% about money. Whether you treat everyone the same whether you have to accept the underpaid guys to leave.
I can't work in a place where I am working hard and get paid half what the others receiving.. It is unfair.
If we take it from another perspective, AFAIK Mane is doing many charity actions in his native village, not sure how accurate that was but to say that he isn't "hungry" about the money.
I think you are right, Mane is not hungry for money to eat because I have heard that he is a generous person who gives part of his salary to charity. He is a great footballer, and he has spread compassion for those who need his help.
I could think that he wanted a raise at Liverpool but it seems that desire was turned down so a good option for Mane would be a move to Bayern Munich or to another team that wants his services. At Bayern Munich he will probably get a good salary offer, so that will help him a lot even though he is also a human who needs food, fame and fun.