Pugs were bred the way teddy bears evolved. Humans find things cute if they have short muzzles and big eyes and generally look like babies. Commercial selection pressures in teddy bears have resulted in modern teddy bears having very short muzzles and big eyes compared to early 20th century ones, because that's what people buy. Lap-dog and -cat breeding has repeatedly led to similar results. Where most dogs historically were bred to be useful for something, even say poodles were originally bred as retrievers, whose woolly fur would stop them from getting arthritis when swimming in cold water to get ducks or such, pugs and squash-faced cats were just bred for cute . . . and ironically may be better adapted for survival than most breeds because while our needs for working dogs may shift or go away with technology, our instinct for cute doesn't change much.
That dog in the manga, though, is bizarre even by pug standards; I keep wondering if it's actually a tentacle monster wearing a suit.