Will this action also delete runs started by the run referenced or will each run need to be explicitly deleted?
So if Run A starts Run B which then starts Run C. When I reference Run A in this action, will Run B and C also be deleted?
No. Both the data deletion action, as well as the data retention policy configured for a given workflow (https://help.catalytic.com/docs/data-retention/) will only target the specific instance (whether explicit, in the action's case, or implicit when based on the schedule of the data retention policy).
If the instance in question has a parent or child instance, those will not be touched, and must be deleted via a separate action, or by configuring the data retention policy of the related workflow.
NOTE: If an action uses inline actions (https://help.catalytic.com/docs/inline-actions/) then the inline workflow defined will inherit the data deletion policy of the parent workflow you are building. If a workflow is used by name, ID, or field, then that workflow must manage its own data deletion policy. This only applies to the deletion triggered by the data deletion policy. If a policy is not configured, then all instances must be deleted manually by the action.