That much I understand, if you stop ASML exporting to China (which is, as you've said a company based in the Nederlans), you stop China from having advanced industry - and are setting them back probably at least a decade. Developing EUV lithography is an incredibly hard process. Now, mind you, preventing them to do upgrades, to what they might have a contractual obligation, is a big deal. You're asking them to take a law suit, and the US has, AFAIK, no means to force a company from NL to take a huge loss.

I'm interested in how will this impact the rest of the world. Are the factories in China used to the rest of the world? Will this impact the global economy in any way? Also, what happens to stuff made in China? If Apple is making an iPad in China, does it have to stop because M2 is an advanced chip? What about Razer and laptops with GTX 3080? Again, will it impact global industry?

Finally, on a theoretical note, I still don't understand how do you prevent export of algorithms....

Can someone explain this regarding fabs? Is this to effect TMSC fabs in China? Intel, IIRC has at least one fab in China as well. Is the US trying to ban fabs from China in operating? Or is this just for fabs ran by Chinese companies producing their native chips?

Also, how do you "prevent the export of algorithms"? They don't ship in containers.... Are they to stop sharing mathematical research over the internet, because "bad Chinese people" will use it?