No, it's Chrome/Linux.
GNU/Linux imples Linux + GNU apps. So GNU/Chrome would imply GNU ecosystem with Chrome. I doubt this will be the case. We will see the linux kernel with Chrome technology on top. This is similar to how Andriod works AFAIK.
The BBC has a GeoIP database which they use to determine whether or not you are eligible to use services such as iPlayer. Whether or not they checked if the computers were in the UK I do not know, but they certainly could have done.