Do they exert any physical control (i.e. parts are made and shipped from North America), or is it just "Intellectual Property" and legal agreements that can be ignored?

This is an honest question, I'm trying my best to word it to not sound like a troll.

Yes the EUV/DUV light source itself is researched, developed, and manufactured in California.

ASML was permitted to acquire Cymer in 2013 during the Obama administration under a strict technology sharing and export control agreement with the US government.

The R&D, technology, manufacturing, and all other operations had to remain in the US.

https://www.asml.com/en/company/about-asml/cymer