They probably have a reverse proxy in front of all their http endpoints and that is still up and able to show the unicorn if the backends aren't responsive.
The static content on the error page might also be on akami or cloudflare side.
Unicorn has a slightly different architecture.
Instead of the nginx => haproxy => mongrel cluster setup
you end up with something like: nginx => shared socket => unicorn worker pools
When the Unicorn master starts, it loads our app into memory. As soon as it’s ready to serve requests it forks 16 workers. Those workers then select() on the socket, only serving requests they’re capable of handling. In this way the kernel handles the load balancing for us.
The static content on the error page might also be on akami or cloudflare side.