Amazon's Android Appstore held great promise when it was announced, but the reality has often proven annoying to use. A big part of that was the terrible Appstore app that was used to install purchased content on a device. Today things are getting better in that department. The Amazon Appstore client has jumped from v5 to v7 and has gotten a complete UI overhaul in the process.
The new UI is still recognizable as Amazon, but it looks more like the updated Kindle Fire tablets, and less like something designed explicitly to taunt you.