Top Up Suica (ID Card) with an Amex Card for points

Hi! Suica cards (ID Cards in general such as Pasmo) are ubiquitous.

I'm able to top up my Suica using my Japanese Amex to acquire points then pay in almost any stores. As Amex takes a cut in the transaction, am I entitled to the same amount of points if I were to pay directly via a point-of-sales in a shop?

Is Suica making any money? I don't understand how this works.