What's really interesting about this business model is not the fact that you can buy a car online, it's the price transparency that you create with this: Car dealers often have 10-20 % margin on a car sale, and they make most of their money by providing services to you after you bought the car, so they are usually able to give you some big discounts. Also, as they usually receive a bonus by the car maker for selling a given number of cars, they have a strong incentive to sell more. The money that they make for themselves depends therefore on the margin that they can achieve, which in turn depends on the customer's knowledge of the "fair" price. Having all the transaction prices out in the open would therefore be quite a nightmare for most of them, as it will allow customers to push the price down quite a bit. Especially for small dealerships (that have higher fixed cost in comparison to their sales and receive less bonus as they sell fewer cars than big dealers) this could be highly problematic, while it could be beneficial for the larger dealerships. Truecar has been doing this model for a while, and I guess Amazon finally wanted to have a share of this market too (and the data associated with it).
On the technical side it looks like they're using the JATO database for their search/configuration tool (http://www.jato.com/). A few years ago I also implemented a car configuration website/app for a German startup (which doesn't exist anymore) using this data. The most challenging aspect was the huge amount of possible configurations/options that exist for some models (especially BMW and Mercedes), which would also have very complex inter-dependencies (e.g. choosing package A + B means you can't choose package C except if you also choose D). To resolve this I had to write a dynamic constraint solver: Finally some abstract computer science that was usable in practice :D
As far as I understand, in the US there are usually less options to choose from, which makes extensive configurators unnecessary. Still, it was an interesting challenge.