I'm surprised and a little disgusted by all the stupid brinksmanship on this thread.
Talk of "fighting to the death" shows a complete disregard for what is best for this boy, because a fight like that certainly isn't.
"This isn't about the father's wants though. It's about the child's right to maintain a relationship with both his parents"
This isn't about the child's right to maintain a relationship with both parents. It's about whether and how that relationship can be maintained should the child relocate temporarily.
It's not all or nothing here. They're not going to "kidnap" him (as one hysterical post claimed earlier). They're just going to live somewhere else for a while.
Instead of getting in a lather about 9 year old boys never seeing their father, surely the right approach is to do as Swedes has suggested, look at the possible outcomes, the downsides and how they can be mitigated.
This is real life. Maybe in an ideal world this wouldn't have happened. But in this world moving for jobs is pretty common. And it has happened, and it has to be deal with. Ideally without "fighting to the death" 

"The situation is that there's a 9yo boy who has regularly been spending considerable amounts of time with his father for his entire life. There is undoubtedly a relationship there. If this boy's mother decides to move to the US then that regular contact would cease. That boy could go months between seeing his dad in the flesh."
Yes, but he could spend months living with his Dad during the US school holidays. Imagine how awesome that would be?
Of course there is a relationship there. The relationship between a boy and his Dad. I'm not sure why you seem to think that is so brittle that a few months of not seeing him in the flesh would destroy it.
"After all, his mum and step-dad are going to want to have some holiday time with him as well. It's unlikely he'd be coming back to the UK to see his dad every holiday."
But that's the stuff that needs to be discussed. If they take him so far away, then they absolutely should agree to him spending all his summer break with his Dad. That's how you compromise on stuff like this - by trying to figure out where the areas of useful give and take are. They need to move for a few years and they want him to go with them. But he doesn't need to be there 100% of the time, and when school is out he could (and should IMO) be with his Dad.
"Moreover, unless you happen to live near a major east coast city in the US then flights between the US and the UK can be quite expensive, particularly when you factor in that he's not old enough to travel on his own. Have you seen how much it costs to fly transatlantic near Christmas, for example?"
And this cost being borne by the people taking him away from the UK should be part of the agreement of him going. If the job isn't going to pay enough for this to be possible then they'll need to think again about whether it is worth taking.