First off, I don't buy the underlying premise because the US has been launching satellites with global coverage for 50 years... I don't see why China would wait until now to respond.
But for your question, with LEO satellites you don't really target specific countries. They cover every country within a given latitude range. A round LEO orbit that goes over the US must also go over China.
However you don't need geostationary orbits to target a given part of the globe. Molniya orbits do the same thing more or less and work better if you want coverage further away from the equator. They were popularized by the USSR and the US and China use them to varying extents.
The SDA satellites are barely skimming Earth's atmosphere and may eventually take a more "active" role intercepting missiles and even targeting the ground, at least that's according to the SDA program's founder,
https://breakingdefense.com/2018/08/space-based-missile-defe...
Lots and lots of satellites that keep passing overhead and you compose the images to abstract away the fact they came from multiple physical satellites.
> In 2002, Griffin was President and COO of In-Q-Tel, a private enterprise funded by the CIA to identify and invest in companies developing cutting-edge technologies that serve national security interests. During this time, he met entrepreneur Elon Musk and accompanied him on a trip to Russia where they attempted to purchase ICBMs.
Yeah, so the lore goes, Musk just wanted to send humans to Mars, and had no intention, originally, to build his own rockets. The first tactic was to retool an ICBM for spacier spaceflight, but the Russians laughed them out of the country.
> In August 2001, Musk shared a plenary talk with Mike Griffin at the fourth Mars Society convention where he announced his plans to send his greenhouse to Mars.[6] In October 2001, Musk travelled to Moscow with Jim Cantrell and Adeo Ressi to buy refurbished Dnepr ICBMs that could send the envisioned payloads into space.[7]
They were not laughing because it was an impossible idea. They were laughing because they have seen an opportunity to part a rich person from his money.
Or laughing because it was absurd, Griffin was CIA. The US had just left the Anti Ballistic Missile Treaty, and so it was obvious to everyone they wanted to develop low cost launch for a Brilliant Pebbles reboot. Now it's finally happening.
There's only one company with that capability and that's the only organization in the world ever to achieve first stage (and soon all stage) reusability for LEO launches.
Because to achieve that you need to put a lot of stuff in orbit and the only way to affordably do that is cheap (reusable) launches.
The technical change is that you can build very useful, very small sats, which are cheap. Current SpaceX launch costs are lower, but like 1/2 price and 2x is not a big premium for a national security need.