Thanks for getting in touch, Zequé.
It sounds like you're having some trouble watching a particular channel on your Apple TV. We can help.
You've definitely taken some good steps so far in trying to isolate the issue. If you could tell us more about your set up, that would probably be useful to narrow down the cause. But, in general, content that is available on the AMC channel could be DRM protected, which would explain why anything sent over AirPlay has audio but not video.
The part that we need to understand is why you're getting an alert about AirPlay when you're sure you aren't using it, and have turned it off.
Are you connecting the Apple TV to a SMART television? If so, are you doing that using an HDMI cable, or wirelessly? If wirelessly, try using an HDMI cable instead.
Another consideration is if any other channels are doing the same thing. If not, the issue might be with AMC, and you might need to reach out to them.
Let us know what you can, and we'll continue from here.
Take care.