This isn't just a joke about Grace not knowing proper terminology at this point. I mean, it is that, but it's also somewhat autobiographical. When I was in elementary school, we all said "play", and that was fine. Everyone I knew was cool with it, that's what you said, and nobody laughed because playing was serious business.
Then I got to Junior High (11-12 years old), and nobody told me that I needed to upgrade my terminology to the "no, really, we're all grown up now" terms like "hanging out". As may be easy to guess, there was one incident of me making a fool of myself in this manner. It only happened once, however, as there was no mistaking that "play" was no longer acceptable.
It does seem silly.
"Hey, you wanna come over and play?"
"Dude, don't say it like that!"
"But I'm literally inviting you over to play games with me."
Commentary added December 22, 2014