The webpage on the partnership actually says you have access to Clubhouses when you are ticketed on a non-stop flight to the UK, not merely going to the UK; the phrasing is a bit weird but I can’t think of any purpose other than to exclude these itineraries.
my guess is they’ve worked the numbers so the Clubhouse can handle the number of outbound flights from the airport it’s located in. Those direct flights also tend to be more expensive itineraries which has to help with the economics.