Both my big macs love to rough house. The claw is a game we play where I dangle my hand over their head, tell them "I'm gonna get you." Then grab their face/beak and wiggle it, while they "beak me" in return. Also make your fingers into a "mouth" and beak wrestle. These games usually involve rolling/flopping around on my lap... with lots of happy squealing and birdie laughter. (Usually because I start laughing.)
The spider game is a good one... mine just grab my fingers anymore.
Maggie (my greenwing) likes toddler games like peek a boo.
She plays ball (with a wiffle ball.)
She can throw with either hand or her beak. Doesn't catch very well, but will play fetch. (My amazon does this one as well.)
She plays tug of war with a rope. (dog toy) Sometimes she'll let you pick her up and swing her by the rope.
She gets down on the floor and chases Sarah around the house like a puppy...
Maggie hangs upside down and "beak wrestles" with my face, nose to beak.
She also sometimes grabs my car keys, runs off with them, and tries to play keep away/Can't catch me... (My red front has been known to obsess over my car keys as well.
My red front also sneaks up on me, pinches me, and then runs away laughing... (That's her version of the "chase me" game. She starts it.)
There's an odd whispering game that she actually initiates with us, where she'll whisper something to someone, and you whisper something else, and then turn her head and whisper something else to someone else in the room, and back and forth around the room we go...
And then there is also trick training, and doing their tricks for you "showing off" they're like proud little kids... look what I did!
Anything that involves your mac being the center of attention, really, will be enjoyed, and will become a bonding thing...