Github enterprise cloud is on github.com and with more features: http://github.com/account/enterprises/new
They don't host github enterprise server for you (though gitlab has something called gitlab dedicated which they host gitlab ee for you).
Why is there an eu github status then ? https://eu.githubstatus.com/uptime
> X-Stat header that controls whether the server operates in enterprise mode.
Perhaps this header mentioned in the article is related, maybe that's the toggle for the enterprise mode? Seems there is at least traces of "enterprise mode" on the normal github servers.