The dude refused to leave the kitchen of his restaurant when they were up for the Michelin review while his wife was in labor.
.
I have no strong feelings about Gordon Ramsay, other than his face is not appetizing, and this isn't in any way a defense of his behavior in that clip or elsewhere - but that "staying at work" phenomenon is quite common and has to be contextualized by the couples involved - soccer players have played the world cup, olympians have competed for gold, husbands have gone to sign house closing contracts and so on and so on. It can be a very reasonable - and perhaps the right thing to do.
A Michelin Star is going to have a gigantic effect on their long term income and life and the legacy they're building for their child - and if the parents are agreed that it's in the best interests of the way they live their lives - then it should be up to them, but it's not at all (on its face) indicative of any moral failing. If he'd stayed in the kitchen because they had some lame celebrity guest, or because truffles had arrived unexpectedly, then sure, but in this specific case, a Michelin star is not a trivial thing - and I'd be surprised if his wife hadn't
told him to stay.
I wasn't there, so I have no idea, but I can tell you that if I were in a similar suituation, I don't know what I would do, but I do know what my wife would say, because she'd think about it holistically and rationally and realize that the better thing for her and the child, would be the long-tewrm benefit. Again, I'm not sure what I'd do but inn a world where we did agree to it, she'd have family and friends and I'd Facetime in if I could and so on.