They keep the instances in a "stopped" state, which means keeping the EBS volume around (and paying for it) but not paying for the instance (which could be another machine when turn it back on, which is why you can't load it into scratch space and then stop it).
What's on the EBS is their docker image, so they don't have to load it back up again.
Makes sense. I still think it would be cheaper to just reload it from S3 (straight into memory, not using EBS at all) on every boot. The entire OS shouldn't be more than a gigabyte which is quite fast to download as a bulk transfer straight into RAM.
Yes it would be cheaper, but the whole point of this article is trading off cost for faster boot times. They address your points in the article, how it's faster to boot off a warm EBS instead of loading from scratch.
What's on the EBS is their docker image, so they don't have to load it back up again.