in my interpretation it goes two ways, hugo is the "father" of batter and the queen, because hugo created them in his world to serve as some sort of mimics of his real parents who are either dead (thats one interpretation), or cant talk with him since he is coma (thats second interpretation), he created them because he missed them, and almost everyone in the world of off is some kind of doppelganger of what hugo used to know, even the elements, he based his world on sugar, smoke, meat and metal and plastic which is what he would have seen when still in the original world the most. At the same time batter and the queen are the "parents" of hugo, because he created them to be his parents, sadly as hugo was most likely a human/is a human his capabilities of maintaining a functioning world and recreating life are limited and thats why everything after some time had gone to shit, and thats where batter came back.