Brown admits to being aware of NFL policy and regulations yet decided to post the video anyway. However, he has issued an apology, he should be fined the regular amount and it should be left at that. The instance hasn't directly harmed anyone, though Antonio Brown may find there to be some subtle, lingering trust issues between his teammates and/or coaching staff in the future.
The NFL is not nearly hard enough on the conduct of their players. There are so many players that are bad examples in so many different ways for the young fans that look up to them. The coach should have been able to say something without the player running with it and causing a stir.
Teams will use this to get fired up, and coaches do grasp things like this, even if they are 16-0, to get fired up. Brown is a naive for this video, and even if Belichick doesn’t use it, others in the locker room will.
You can only buy into the same motivational speech without changing it for so long, so new material is loved, and free material like this is thanked.
Antonio Brown is not being treated too harshly for putting his video online. If anything, he is being treated with kid gloves. Back in the good old days of football, had this happen, his teammates and coach would've destroyed him. These days, you just can't hurt the fragile egos of highly paid athletes.