Obviously, family life goes on, but it's only been three days. If he'd just put in a discreet application with everybody else and then the successful applicant had been announced and it wasn't him, such behaviour would be over-dramatic indeed.
But apart from probably having made mental plans based on the job he was told would be his, he's been professionally and personally humiliated in front of his colleagues (not to mention his extended family) and he may be concerned that they might jump to conclusions as to why the sudden change of plan e.g. "I wonder what skeleton they found in Mr Conceal's closet to make them take his job offer away - there's no smoke without fire, you know." Totally irrational, I'm sure, but these are the kind of worries that go through people's minds in cases like this.
It's very frustrating for you, especially as it's falling to you to hold things together at the moment, but don't take it as a personal slight to you. Don't be afraid to gently share with him your struggles and concerns for you all as you get through this; but whatever you do, don't use the phrase 'pity-party' in front of him.
I'd try to show compassion and just be there for him. Talk to him about his feelings but don't directly bring up the subject of the actual act of betrayal; but provide a willing and sympathetic ear if/when he does feel the need to replay it as he tried to make sense of it all. If you can, maybe try to engage him gently in getting back to normal again and make sure he's in no doubt that, whatever his workmates may have done or said, his family love and value him as much as ever, are proud that he did all he could to try and get the promotion and are behind him all the way.
And, when his confidence and security in his self-worth have started to recover, maybe suggest that he explore other avenues where his skills and experience would be more appreciated and he (and his feelings) be valued as a person by people with a significantly more professional outlook on their own jobs.
This has clearly hit him hard, but the feeling of having been cruelly set up for a kicking will pass and he has nothing whatsoever to feel ashamed about. Maybe if, in time, he does decide to move to a company more deserving of him, it might just make them take stock as they realise what - and why - they will lose when he goes.