My view is arranging the playdate is structured. What they do is unstructured but Levine's book was about total unstructure, at least that was my interpretation.

The child that goes out on its own, finds kids to hang with or not and then they originate their own play was all crucial to development of self esteem.

When I was DD's age, 9, I went to the store, crossing busy streets, figuring out the optimal choice of penny candy for my dime or bought bread for my mother at the grocery store next door. I found friends and we created games, we would go to someone's house, find cookies, make Kool-aid on our own.
Make sandwiches. Parents were often somewhere in the neighborhood but I do not remember a parental presence very much.
We grabbed our Barbies and went to someone's house and created a Barbie village. We had to be far more creative, we had a lot less stuff. We took far more initiative than DD when I arranged a playdate yesterday and today. In Levine's view, the playdates are structural activities at this age, not enough initiative for the kids.