It's a genetic fact that "beissers" are closely related to other mastiffs, which includes everything you could hope to say is an alaunt. Beissers are just highly specialised purely for gripping and subduing large game, while other types of matiffs from the "cattle and swine" side are less specialised. Believe it or not terriers are also closely related to this lineage. But bulldogs or beissers especially could accurately be described as a specialised variety of mastiff, this is what the genes show. English mastiffs, neo mastiffs, fila brasileiros, presa canarios, etc etc are all quite closely related to boxers and ambulls and pitbulls and cane corsos. Meanwhile ovcharkas and gampyrs and the like are somewhat closely related to the above breeds, but less so than they are to eachother. Indicating the "cattle and swine" lineage split off from the "shepherd's mastiff" lineage some time ago, and has since split into more specialised varieties like beissers/bullbreeds, but also retained some less specialised varieties (typically heavier and better guardians but less elite at gripping and subjugation).

BTW my understanding of the alaunt is there were 3 types -

alaunt boucherie - "Beisser" or bulldog type, eg- alano, ambull

Alaunt Gentil - Running mastiff type (infused with sighthound), eg - great dane, bull arab

Alaunt Veantre - Heavy boned hanger - eg- presa, fila

Basically all big game hunting dogs with different degrees of specialisation in different departments. None of them shepherd's mastiffs or lgds. 

These were the "alaunts" of medieval europe, a different thing to the dogs of the alani people. Which you're right probably were most like a primitive proto LGD type or big shepherd's mastiff. And indeed this type was at least in part ancestral to all of the above types. But alaunts were a more recent thing. The alani people didn't call their dogs "alaunts", I'd wager they called them whatever the alani word for "dog" was. The spanish and to a lesser extent the british and french called their big game hunting dogs alaunts around 14-1600 AD. Apparently as a homage to some notorious dogs from the alani people, but only incidentally partly descended from them and by then very different in form and function. 

This is my take anyway.