From what I can see, the terms of the deal haven't been changed. The cost is still spread over 5 payments, with the first payment due when you check out. A credit check is not required, but Amazon does want to see a credit card.
I can't say that I am surprised to see the program is still around, but I am a little surprised that it's been running for 3 months before the blogosphere noticed. That's odd.
It makes a lot of sense for Amazon to offer this program. Once they have maxed out their retail channel by selling to everyone who can pay full price, and lowered the price as much as they can via ad subsidies, the next logical step was to offer an installment plan and lower the purchase barrier another notch. And since Amazon handles their own payment processing, the actual cost (compared to having the stock sitting in a warehouse unsold) is minimal.
What's more, if the reports that Kindle owners spend $443 more per year with Amazon than non-owners then the retailer would be a fool not to offer this plan.
But I wouldn't put too much weight into that report; this installment plan is mainly for people who can't afford the full retail price of a Kindle or Kindle Fire in a single charge. If their funds are that tight then I'm not sure how much they can afford to spend to spend at Amazon.
On a related, Amazon has been trying out a program which lets customers try a Fire TV for 30 days before paying. That program is much more selective, though.