In the given sentence, the word "quaint" is used to describe the free, natural play enjoyed by Americans around the author's age, particularly baby boomers or older. In this context, "quaint" means old-fashioned, charmingly simple, or reminiscent of an earlier time. The author is suggesting that the type of play experienced in the past now seems outdated or nostalgic in comparison to the technology-driven activities of the present era, such as kid pagers, instant messaging, and video games.