Renter's insurance is a 'Drywall to Drywall' type of coverage. So it will replace your personal belongings, but will not repair walls, doors, lighing fixtures, ect that are part of the actual structure.
The Apartment building's insurance will cover all the damage to the common areas, and any inside structure damage to the apartment's.
However, it is not like a homeowner's policy. You can not 'sue' the person's insurance to get money to pay for repairs.
I would also imagine that the person who did that will be sued by the apartment building and will have to pay back a bunch of money.