Yes, you'll be able to unlock an achievement for watching TV with Xbox One, by linking your cable box through the HDMI input. And that's not all. "We're going to have more achievements for media experiences in general," Xbox's Yusuf Mehdi told us. "You're going to see more of in a lot of different places."
In a new screenshot released by Microsoft today, you can see exactly how achievements in entertainment apps might work. In addition to the usual one-off achievements, there will be time-based "challenges" that can encourage you to watch a specific show. In the case of Amazon Video, it would be Betas.
Achievements in entertainment apps won't affect your Gamerscore, however. "Only games will give you Gamerscore," Major Nelson pointed out in the summer.