Good question!!!
Intelligence alone is a survival factor. But along with intelligence comes boredom (I would think) and so playing may be a result of that...
Recommended viewing:
The Wild Parrots of Telegraph Hill:
The Wild Parrots of Telegraph Hill Film
The Real McCaw:
The Real Macaw - Introduction | Nature
Kea - The Smartest Parrot:
Kea - The Smartest Parrot - DocuWiki
Parrots in the Land of Oz:
Parrots in the Land of Oz - Introduction - Australian Parrots | Nature
You can find portions of some of these on youtube and other streaming sites - or wait for them to come 'round to pbs...
Amazing birds!!