When I was young and played with other kids, we never called such times "play dates"--we just went to kids' houses to play. Now when I talk with parents or kids, they'll tell me that they have a play date with someone instead of saying that they're going to play with their friend.
When I looked it up in Wikipedia, there was one sentence that was a sad commentary on modern life (they said "Playdates are a late 20th century innovation"):
the work schedules for busy parents, along with media warnings about leaving children unattended, prevent the kind of play that children of other generations participated in.
It reminds me of a recent conversation I had with a mother, who said she and her husband chose to live in a small town far away from Chicago because their kids can ride bikes and do other things without worrying about bad things happening. It's just sad that the sickos have to ruin kids' play time and some people are so busy they have to provide a formal word for something that kids naturally do.