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
However once you get big enough, the cost savings usually start falling the other way. Several companies I've been at have moved from using hosting to running their own boxes, either co-located or in their own data center (the CTO like to call this, "moving to our own private cloud" or some other marketing bullshit). Even then, careful decisions are made on to what to host locally and what to keep on a managed service due to cost.
The hyper.sh API address is us-west-1.hyper.sh, which looks like the AWS style, however, it is not an AWS address and it is located in an independent IDC around Los Angels.
Original: Not on AWS at all doesn't seem possible
The docs for Floating IPs [1] list 52.68.129.19 as an example, which is an AWS Elastic IP.
The docs for the API [2] says "Hyper.sh API signature algorithm is based on AWS Signature Version 4", and then proceeds to explain the differences, which is variable names. The API Domain is us-west-1.hyper.sh, which is the same URL schema as AWS (us-west-1 is also AWS's North California region).
Maybe the containers themselves are somehow not on AWS? Sure. But not on AWS at all doesn't seem to be the answer.
1. https://docs.hyper.sh/Feature/network/fip.html 2. https://docs.hyper.sh/Reference/API/2016-04-04%20[Ver.%201.2...
At last, you can try it. Then you will found it is totally different from AWS.
http://ark.intel.com/products/92981/Intel-Xeon-Processor-E5-...
Take the Xeon E5-2403[1] and the Xeon E5-2637 v4[2]. Both are quad-core Xeons, but they differ by pretty much everything except core count.
Here's a comparison of their performance: http://cpubenchmark.net/compare.php?cmp%5B%5D=1827&cmp%5B%5D....
Granted, this is an artificial benchmarks, but the results speak for themselves. In this case, the Xeon E5-2637 v4 is almost three times faster than its little brother, the Xeon E5-2403.
Quantifying CPU performance by number of cores is disingenuous at best, and dishonest at worst.
[1]: http://ark.intel.com/products/64615/Intel-Xeon-Processor-E5-...
[2]: http://ark.intel.com/products/92983/Intel-Xeon-Processor-E5-...