Original: I'm pretty sure they're entirely hosted on AWS. Given that they say they're hosted in Los Angeles, I think they mean us-west-1.
Their API uses an AWS address as their endpoint, their authentication is just a veneer over AWS's authentication (including basically find and replacing header variables). They previously had docs that showed how to add floating IPs to the containers, and all the IPs were AWS Elastic IPs.
I'm pretty sure the docs specifically stated they were on AWS last time Hyper came up [1] (Hyper.sh had linked off the Hyper article), but now when I look it's not there. So either in a few days they've moved their infrastructure off AWS and just left their API up there (and are doing some crazy stuff to redirect elastic IPs), or they moved everything but their API off Amazon a while ago and hadn't updated their docs, or they've decided to make the fact they're on AWS less visible, while they're competing with Amazon's own container service. I have the feeling it's option #3.
To answer your question though, I think they're using M4 AWS instances [2], so Xeon E5-2686 Broadwell or Xeon E5-2676 Haswell. Probably the m4.10xlarge, since they talk about the 10 GB networking the containers use.
1. https://news.ycombinator.com/item?id=12873089 2. https://aws.amazon.com/ec2/instance-types/#m4