Releasing stuff isn't simple, the hosted services only work because of the rest of their infrastructure. Writing about the tech is usually the best way to spur clean open-source versions that we can all use.
From what I recall DynamoDB is a somewhat hacky API layer over a bunch of MySQL clusters. I'm not sure anyone would, or should, attempt to use a non-managed version of it.
The recent MySQL info comes from this 2016 thread on DynamoDB storing empty strings: https://news.ycombinator.com/item?id=13170746
Confirmed by this comment specifically: https://news.ycombinator.com/item?id=13173927
The latest 2018 ReInvent deep dive on DynamoDB doesn't reveal anything but still fits if mysql is powering the storage nodes: https://www.youtube.com/watch?v=yvBR71D0nAQ
But there is more to this as well. AWS is a huge ecosystem by itself, a lot their services intertwined with each other, simply open source DynamoDB isn't enough without open sourcing the networking/storage functionality that is probably provided by other services.