How to watch a movie I rented on my Macbook on my iPad?
From the same support document:

If you rented the movie on your computer, but want to watch it on an iOS device, connect the devices and sync using USB. When you move a rented movie from your computer, it will disappear from your computer’s iTunes library. You can move the movie between devices as often as you want, but you can only have it on one device at a time.
If you rented the movie on your iOS device or Apple TV, you can’t move it to any other device.
To watch an HD movie, you need to play it on a supported device: your computer, iPhone 4 or later, iPad, iPod touch (4th generation or later), or TV using Apple TV.