Yes they are. They are not 100% responsible no but it's the main party as it provides the platform and encourages the behaviour. If their platform has become unsafe and causes harm that's the bit that they are responsible for. It's the same thing as suing a car manufacturer if the car was designed / built with a safety flaw.
> The playground builders are usually not considered responsible when bullying happens at a playground.
That's a great point thanks for making it. By "playground builder" I assume you are meaning the company/org that built the playground and actually they are responsible for the safety of the equipment and if a child gets hurt because of their negligence they will be sued. In my estate we have to pay for insurance for this express purpose.
In terms of bullying though you don't use playground equipment to bully someone. Bullying on the school grounds is the schools responsibility and they have a duty of care to the child to help. So just because the builders built the school doesn't mean they are responsible for all actions that occur only on defects on their work that cause harm.