Use it when you doubt someone's actions and need an explanation for their unexpected behavior. He's been very secretive with his phone lately. What is he playing at?
Pro Tip 2/3
Informality
It's casual and might be rude in formal or serious conversations. Use with friends or in laid-back settings. She's taking another break? What's she playing at, we've got work to do.
Pro Tip 3/3
Colloquial Nuance
This phrase often carries a tone of frustration or annoyance with the other person's behavior. They promised to help us but now they're backing out. What are they playing at?