Amazon Underground pays the app developer for the duration of usage of the app, and so needs to track how long you are using the app for. Perhaps it needs data tracking enabled to identify the duration of usage?
Did you read the screenshot? That's exactly what Amazon says it needs data tracking for.
(For those who haven't read the article: The author only discovered this because they have CyanogenMod and a permissions blocker installed and in use. Most people wouldn't be told they were being tracked.)
It's actually just a setting in the Amazon Underground app to disable tracking of apps. The "actually free" apps require the setting enabled. He disabled it and it's telling him that. The CyanogenMod/Privacy Guard/Location stuff is all unrelated.
I can't see where the article's scary headline is justified. It appears that all that happened is, he used this service without knowing it was based on tracking app usage, and was surprised when he found out.
Agreed, but it is pretty surprising, and most people will have no idea this is what's going on. I couldn't find it mentioned on the Amazon Underground homepage: