It's a bit like how the US Cuba sanctions worked and why they effectively isolated Cuba from everything.
I still don't see any way to read that as saying they could only do business with US customers, whether they give in or not?
The courts have historically been pretty consistent about giving the DoD whatever the fuck they want, going back to WW2 and even longer for the predecessors of the DoD. I agree that the next administration might reverse it, but the thing is, the government will stay irrational longer than Anthropic will remain solvent.
The US government told every American company to stop doing business with Huawei and they all did it overnight, even when it cost them billions. TSMC stopped fabricating for them, Google pulled Android licensing… The machinery of sanctions compliance is extremely well-oiled and companies fold instantly because the outcome of noncompliance is literally getting thrown in prison.