Yes. Typically what you see on the sites is a 'Buy Now' which is Amazon and the 'Add to Cart' which will allow the other payment types such as Paypal and google, CC through Mals. You do not give Amazon a cut if they use the other Payment types.
In the past it was available to send everything to my cart and amazon was just one of the choices from there but Amazon took away that functionality. ( plus a lot more )
These days I encourage people to try to turn off Amazon and turn on openlibrary.org and see how the website looks. There is no effort involved in switching back and forth.