Obviously trying to cut through NYT's regurgitation of legal details is fraught with problems, but I'm guessing the original court order just basically meant he could move back into the room, pending the hashing out of a formal lease conforming to the Rent Stabilization Act or further legal action. But Barreto (supposedly) took it to mean more than that, and parlayed the order into filing a fraudulent deed which then took much time to clear up.

Taking the narrative at face value, it seems like the root of Barreto's mistaken reasoning was thinking that "possession" means ownership. Then it snowballed when thinking that NYC's refusal to record a deed for a single room entitled him to record a deed for the whole premises, combined with a fundamental misunderstanding of the semantics of deeds (just because you're able to get something recorded does not mean it conveys ownership).