At minimum, root volumes for the VMs. Theoretically, you could load immutable machine images from the network and run entirely off of in-memory filesystems if you persist nothing past instance shutdown (similar to how extremely cautious people might run Tails booted off USB on a laptop with no hard drive), but that won't actually save cost since memory is more expensive than disk anyway.
I don't think you can even technically do that in AWS. I don't think there is any way to detach the root volume from a running instance, or use an immutable network image to boot from. However, for many server workloads, operating entirely would be reasonable. Often you just need the operating system kernel and your server software, and maybe a monitoring agent. And all of that will be loaded in memory anyway.
Well, not to answer your question with a question, but what would you imagine backs all of those database services? Or, said another way, I'm not sure Corey Quinn is mapping the cost dependency graph correctly by giving this breakdown as mutually exclusive (from the standpoint of AWS internally).
Is Amazon’s general architecture for their retail site publicly described anywhere?