The frictional force exerted by the floor on the person's feet is a centripetal force. But that's just terminology.
You are looking at this problem in terms of balancing torques. That is a valid way to proceed. You have chosen to use an axis of rotation at the person's center of mass. That is also a valid way to proceed. You have correctly identified the horizontal frictional force of the merry go round on the person's feet is one torque about this axis. You have correctly realized that gravity does not produce any torque about this axis.
But there is another force being applied to the person. Can you identify that force?
Edit. I see you have realized this yourself.