My ex plays games during dropoff time

Rather than stand there complaining, I'd say you would be wise to wait inside. There are no laws that govern how long it takes to eject the offspring from the car.

Yes. Stay inside.

Absolutely. There's nothing rude about waiting for your child to get out of the car, or even to your door, before scooping her back up. As long as she is IN his car, it's still his time even if it is a few minutes longer. Stop standing outside the car and waiting. They are BOTH extending their time together, your kid knows the routine and if she wanted to leap out of the car and rush up the steps to "home". Then that's what she'd be doing She is ALSO lingering with Dad. You get a lot of more of her time, don't you? Let them have their time, they know where the front door is.

He plays games because he's getting the reaction he wants from you. If you stop playing the game he'll get bored without the reaction.

Why do you feel compelled to come out of the house and stand next to the car like a dolt? Just wait until they knock on your door.

No reason at all for you to go outside, if no one has knocked on the door. Let them wind up their visit as they desire, and either he will knock on the door to announce she's' home, or she will (and hopefully he'll wait until he sees you open the door before he leaves).

There's no reason for you to go outside and stand, waiting. He's not "playing games". He's not responsible for you choosing to go outside and wait by the car. He may intentionally take his time, because you are waiting, but the being outside waiting is your choice.