Wiktionary
vb. 1 To pretend to be a different person while playing a game. 2 To give the impression that one is not working in a professional manner.
Usage examples of "play at".
Then, in 1960, Nathaniel Branden asked me to let him give a reading of the play at Nathaniel Branden Institute, in response to requests from students.
His hope was that Sir John was gentleman enough merely to play at the game, without trying to push it through to its logical conclusion.
Superheroes in the Doll CornerMollie Is Three: Growing Up in SchoolBad Guys Don't Have Birthdays: Fantasy Play at FourThe Boy Who Would Be a HelicopterKwanzaa and Me: A Teacher's StoryYou Can't SayYou Can't PlayVivian Gussin PaleyHarvard University PressCambridge, Massachusetts, and London, EnglandCopyright 1992 by the President and Fellowsof Harvard CollegeAll rights reservedPrinted in the United States of America10 9 8First Harvard University Press paperback edition, 1993Library of Congress Cataloging-in-Publication DataPaley, Vivian Gussin, 1929You can't say you can't play / Vivian Gussin Paley.
She knew that if she had been given a part in the history play at the beginning she would never have had the chance of such a big part.