When Leonidas sets the permissions shown here as one of many users on a Linux server, what type of access control model is he leveraging?

The Linux filesystem allows the owners of objects to determine the access rights that subjects have to them. This means that it is a discretionary access control. If the system enforced a role-based access control, Leonidas wouldn't set the controls; they would be set based on the roles assigned to each subject. A rule-based access control system would apply rules throughout the system, and a mandatory access control system uses classification labels.