No, Amway was a multi-level marketing system that paid people for getting others to join. Amway would get a chunk of the money from the products they sell to members. It was a concept where money flowed upstream. Making the people who got in early extremely rich without having to do any work.

With Firefox there isn't any money involved, so it isn't anything like Amway.

It's more like Pepsi, really. Asking someone to switch from Coke to Pepsi and offering to give them a free case of Pepsi for doing so. Pepsi loses money on the deal, but they gain more customers. See the difference?