I don't think it is vague. It makes it clear that the lounge access rules cover lounges operated by airports and other airlines: therefore a guest is allowed in a third party lounge.

Having said that, the lounge access rules often contradict each other. For example, the rule about whether the guest has to be on the same flight, same airline, or any oneworld flight, varies according to where you look. So one can hardly rely on any given web page being the last word in the matter.

On the couple of occasions I can think of that I've taken a guest to a third party lounge, it wasn't a problem at all.