The stepson is paying rent and should have the right to order food whenever he pleases. It's not his fault that DoorDash drivers ignore the delivery instructions. He deserves to enjoy the comforts of his home without draconian restrictions on when he can satisfy his hunger.
Paying rent does not give anyone the right to disrupt an entire household. The stepson is showing a blatant disregard for the well-being and schedules of his step-parents. His argument is nothing more than a selfish justification for his inconsiderate behavior.
While paying rent does afford the stepson certain rights, it does not supersede the need for respectful cohabitation. The repeated late-night deliveries, despite explicit requests to cease, demonstrate a clear disregard for the household's peace. The stepson should find a way to receive his midnight snacks without disturbing everyone else.