I think you summarised it very well here. Just talking about phenotype a game bred apbt might be a sub-type and that´s where the confusion comes from. At least some lines due to heavy terrier influence differ in phenotype from a "typical" butchers´ dog. (A Cane Corso, a correct Dogue de Bordeaux -hard to find-  etc. would be one.)

However in behaviour & temperament they fit into the butchers´ dog role, more than into others.

Actually I would say and I guess here many people will for all days disagree with me, that some or even a lot of the best fighting dogs were dogs of the royalty and are typical Veantres! Just also alive, before the "veantre-name" was alive. Better suited than LGDs from the mental side and physically obviously without any doubt superior to the butchers´ bulldog.