Problem in playing my rented movie on iTunes

Hello alya101,

please reference below please :)

Watch your rental on any device

• You can watch movies that you rent on any device that has the Apple TV app and is signed in with your Apple ID. 
• You can download your rental on one device at a time. If you download your rental on one device, you can stream it to one other device simultaneously.
• If you can't play your rental, see if it's downloaded or streaming on another device. To download your rental on a different device, remove the rental from your device, then download it on the device that you want to watch it on.

*You can't download rentals to your Apple TV, smart TV, or streaming device.

• If you can‘t stream or watch video content from the Apple TV app, restart your device. If your rental still won't play, learn about streaming issues or report a problem.
• For downloads, you can start watching your movie as soon as enough of it has downloaded to play without interruption. If you plan on watching your rental on an airplane or where Wi-Fi isn't available, you might want to download your rental a day before to make sure that you have enough time for it to download to your device.

I hope this solved your problem!