If any mastiff "breed" from today has anything to do with that statue, then they all do. They all share a common ancestor from after that (or around that time, but yeah probably later).
ESPECIALLY if they're in the same area, are you really saying some obscure cane de presa meridionale descends from that statue's "muse", but cane corsos and neos don't? Obviously that dog is very very very closely related to neos and ccs, I'd be inclined to say it's a neo or cc cross personally.
It also should be noted there's no reason to look to italy when you think of roman dogs, rome wasn't italy, it was most of europe and part of asia and part of north africa. All dogs in that area likely descend in part from "roman" dogs. Italy is just another part of rome.
Also dogs from everywhere the spanish and british colonised descend from roman dogs as well by extension.
A fila brasileiro is as roman as a neo mastiff, an american bulldog is as roman as a cane corso, a bully kutta is as roman as a "cane de presa meridionale".