play atphrasal verb
Definition of play at
1 : to do (something) in a way that is not serious They were only playing at trying to fix the problem.
2 chiefly British : to play by pretending to be (someone or something) She liked to play at doctors and nurses as a child. —often used in the phrase play at being (something) boys playing at being soldiers
3 British —used to say in an annoyed way that one does not know the reason for someone's behavior What is he playing at?