I see now.
Well, Amazon's module does not consider an option of adding it to the checkout page (probably because of legal or marketing concerns) that is why all payment logic is located in the classes/XLite/Module/Amazon/PayWithAmazon/Controller/Customer/AmazonCheckout.php file.
If you want to put Amazon payment method onto checkout page, you have to basically create your own payment method. This process is described in aforementioned webinar and it is not that complicated to be honest.
Surely, you can order a customization from us. Just drop us a message at
sales@x-cart.com and receive a free quote, so you could at least estimate the expenses.
Unfortunately, considering current implementation of Pay With Amazon, there is no effortless option of putting Amazon payment to checkout page.
Tony.