As I said, they call their whole video service Prime Video, for example look at this movie https://www.amazon.com/Star-Wars-Skywalker-Carrie-Fisher/dp/B082VZL4T6

It's possible they meant Amazon Prime, but as you quoted, that's not what they said.

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Amazon has offered NFL Thursday Night Football games on Prime Video and Twitch for a few years

They also offered it on Twitch, which I assume was free. I don't think they require you to pay for any live streams (it'd be the first one I've seen that you do) but they might have.