Rent movies from the Apple TV app - Apple Support
You do not need to download to view the content. You can stream directly from Apple’s servers.
“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.”
I did it through my iPhone so I can watch it on my IPad.
You can do the rent transaction on any of your devices. Once the transition is completed, then it will be available on any of your devices with the Apple TV app (or iTunes application), when signed in with the same Apple ID account.