I finished OFF, and here's my interpretation of the story.
Hugo created the Batter and Queen, but they're not married because Hugo's parents were either never married or divorced. The Father, who is the Player, Elsen, and the Batter, kept his son in his room in the city, only bringing him out for the occasional religious event, hence the warped perception of cities and what makes up the world. He was neglectful in that he didn't attend to him often due to work, but he was attentive in that he made him take his medicine regularly and tried to keep him entertained with books he thought a child would like, despite Hugo being beyond them and the books themselves being stupid. Hugo began leaving on his own and stopped taking his medication. The Father noticed this and took the boy to a cabin in the country. While there, Hugo met Japhet (a pseudointellectual and/or student/teacher who gave him books), Enoch (the Father's boss or a local official), and Dedan (a friendly local or elderly veteran/former noble with a significant amount of free time). After telling them his situation, they agreed to support Hugo in staying with his Mother in the country. The Father agreed, believing her to be able to take better care of Hugo, and himself to have failed in doing so.
The Father returned to the city, and the four remaining in the country lived out a life of keeping Hugo happy as he's kept on life support due to his repeated attempts of escape and refusal to take his medication causing his condition to worsen significantly. However, they eventually revealed themselves to Hugo as far worse than his father, who only had occasional outbursts (the Burnt), and Hugo begins to act out (the Spectres). Time passed, and the Father learned of Hugo's birthday party and living situation through his friend Zacharie, who is dating Suchre and provided goods to the Father while he was watching Hugo. Enraged, the Father stormed back to the country as the Batter, with the plan of confronting and removing, likely killing, the men who had replaced him in Hugo's life while facing his own past errors (the Elsens), forcing a confrontation with Hugo's reality as the boy's birth defect, arthrogryposis likely paired with a congenital heart condition, has become terminal (the Secretaries) and an acceptance of how and why the others replaced him (the Add-ons). Upon arriving, he was met by The Judge/Pablo, a local who was the brother of Valerie, now Japhet, a rather foolish pseudointellectual. The Judge helps the Batter initially but couldn't stand the reality of what he was doing when Japhet was killed.
After beating Dedan and Japhet (or Dedan, Japhet, and Enoch), the Batter returned to where he started and fought Sucre, who had decided to intervene in favor of the Mother, now the Queen. Afterward, he fought the Queen, who had taken on a Christ-like role in the boy's eyes despite her active negligence, especially of his desire for immediate affection. He defeated her then confronted a lucid Hugo, who had been interpreting everything so far into a story of his own. The Batter killed Hugo's view of himself as in control and invincible but reassured him that he would not have to fear what came next. The final confrontation with the Judge/Pablo was right before the Batter turned off Hugo's life support, ending the charade on his birthday. The Judge wished for the world to continue, despite him and Zacharie being the only ones left who would have any power, and the Batter obviously wanted to end it, seeking to turn everything off.