What are the implications for back end development? Will this greatly reduce server complexity (need for redundancy)? Could AWS just give you a machine in the cloud, and you wouldn't need to worry about databases and database backups and so on, you could just keep all your data locally in natural data structures?
This would not necessarily affect back end development as you would still want high availability for the application by using an active-active setup across two availability zones in EC2.
With regard to your question on data structures, yes - they would have to change. MySQL and most other databases use b-trees since they were meant to live on disk. Just running MySQL on memsistor-backed storage would result in a considerable waste of CPU and storage capacity (b-trees are not very compact).
Running a database like MemSQL on memsistors would make the most sense since it uses data structures meant for DRAM.