Another benefit to Amazon is that they may choose to "retire" particular issues of the currency....and those that are un-spent then become worthless.
Unless users of the currency have managed to spend up every last Coin prior to the "retirement" they may end up having given money to Amazon for nothing, which may wipe out any discounts offered at purchase.
The production of "scrip" (private currency) is common in a variety of venues ranging from folk music festivals, arcades, carnivals, remote towns, and subways. It benefits the provider by making the currency only usable within their venue. In exchange, they may provide some kind of discount. With widespread "gift cards", users get locked in but they also pay fees and taxes to get the card. This approach removes some of the overhead costs (but still means that the funds are locked into a particular provider without any external guarantees).
The biggest question that comes to mind is "why?" The "it's an easy way to..." really doesn't hold water. Not much is easier than buying things online. I can't imagine it being any more secure either.
What I can imagine is that it's like loading up a store gift card. It's just like real money except you can only use it in one place. In exchange for locking a lot of your money up, they give you a coupon. I'd say this is a pretty old and conventional marketing program just described in a "new and innovative" way.
"This is very different from Bitcoin which sounds like an ordinary Ponzi scheme (if I'm wrong on this would someone please explain why it's different than a Ponzi scheme)."
Be careful what you wish for. There are Bitcoin fans (fanatics?) that will talk your ear off.
It sounds like an ordinary obscured discount, i.e. a discount that sounds larger than it really is. It's akin to S&H Green Stamps (remember them?) or frequent flyer miles. With Green Stamps your grocer gave you stamps that you pasted into a book. When you had a full book you could redeem it from a catalog of mostly useless stuff. The book gave the illusion that you had something much more valuable than you really did. The same thing is true of frequent flyer miles. The real value of a mile is hard to pin down but the apparent value seems very high because the unit is so small, somewhere in the neighbourhood of a penny, but possibly much less. An Amazon Coin has the value that's exactly a penny so 500 Coins is only worth $5. However 500 Coins sounds much larger than $5 because it's not a common unit. If they said you had 500 pennies in your account you would treat it as worthless, after all most people have at least that many pennies sitting on their dresser.
This is very different from Bitcoin which sounds like an ordinary Ponzi scheme (if I'm wrong on this would someone please explain why it's different than a Ponzi scheme).
It's an interesting idea with lots of potential marketing applications for Amazon. But as far as creating an alternative currency is concerned, it just boils down to who do you trust - Jeff Bezos or the US government?