What are you talking about? How could any company dismiss someone for a video of them kicking a cat?! How would that stand up to any kind of employment tribunal?
He probably will have a "bringing the club into disrepute" clause within his contract, however I agree with you that he's very unlikely to be let go for free, or even shunned for too long.
If they did terminate his contract, he'd be a free agent and would just sign up (for more money) somewhere else.
Not going to happen.