OK, I'm honestly confused why I'm getting downvoted here. Can't you use the iPod touch as the companion device to Airplay from for Amazon Prime video?

I didn't downvote you, you're right, I was thinking between an iPad and an iPhone (and I had forgotten that iPad Mini is cheaper). But perhaps people are downvoting you because you are pointing out a technicality when the point is really that to get full advantage of the Apple TV you need some other device that's exclusively made by Apple and that's not cheap.