This is a mid-course interceptor. It's to hit the warhead in space, in mid-flight. I'd assume while it's coasting. They planned to put a site in Eastern Europe to counter Iran's missile program, but didn't in the end. Partly because the Russians cut up rough, but I suspect mostly because it wasn't working yet.
MIRVs are really hard, and North Korea are still struggling to shrink their warhead down to one per rocket size, as well as getting the rockets to work reliably. So I doubt they're worrying about them yet - it took the UK billions, and nearly a decade, to get Cheveline in the 70s, which is similar but cheaper tech to get multiple warheads through ABM defences but isn't fully independently targetable.
Current US strategy on missile defence is multi-layered. Obviously it's all still in various stages of development, so I doubt anyone really knows what will work, or how well.
So you've got THAAD which is already deployed in Alaska I think, and is being deployed in South Korea as we speak. That's the Terminal High Altitude Area Defence System - aimed at hitting the incoming warhead/MIRV on final approach to the target. They're the last line of defence.
They've then got the early shot, which is the SM3. That's a naval SAM, carried by the US Arleigh Burke destroyers and their AEGIS cruisers. Japan also use them. And they're capable of hitting satellites, and missiles in flight. The US have a deal with Japan where there are always a couple of ships in the Sea of Japan to try and shoot down incoming missiles at an early stage, where they're obviously most vulnerable, as they're going slowly and can't manoeuvre. Japan obviously also maintain patrols to do this.
There are also apparently various electronic means of getting at rockets in the early stage of flight, and rumours the US have been actually using them to bugger up North Korean tests. I've no idea how much of that is true, wishful thinking or even possible.
Then you've got these mid-course ones.
There's also someting I can't remember the name of but is basically a land based AEGIS system. It's cheaper, and already proven to work using SM3 - but obviously not on a ship. And the US are talking about putting one of these bases in Romania, to replace the mid-course missiles that would have gone to Poland. But that was to counter the Iranian threat, which is much reduced, as a nice nuclear deal has been signed. It also annoys the Russians on principle, so may or may not happen. But would seem to make sense in South Korea.
However putting that near China might really annoy them, given they've already complained about THAAD - even though that's aimed at blocking warheads, and not Chinese missiles in flight.
Russia has many missiles, so shouldn't be too worried about ABM weapson taking out a small percentage. But China only operates a few hundred warheads, as it has a similar limited nuclear posture to the UK and France. We aren't aiming for global destruction, just to take out your top 10-30 cities.