Yes, I think there should be some form of punishment for Antonio Brown as a direct result of his actions. To livestream people in a locker room like that is a violation of trust. People are being themselves among friends and colleagues they trust. To create a video and livestream without prior permission is not a good idea.
Yes, Antonio Brown should be punished for the locker room video. As a professional sportsmen, Antonio Brown must be held to professional standards at all times. Although he has opponents and should never express his dislike of them publicly. Getting "pumped up" on the field is normal and expected, but using such fowl language is inappropriate at best.
Honestly, I'm sure the Patriots are A-holes, but so are many of the NFL'ers. It seems pretty disloyal to your team and coach to air what should be private team discussions, and I do not subscribe to the 'just locker room' talk or 'boys will be boys' crap, but if you're a team player listening to your coach and coaching staff it's not a great idea to broadcast that.