While I don't want to dismiss OP's concerns, I vicariously enjoy the turnaround of the US having to worry about someone else's extraterritorial decisions.
In practice, though, I don't think it would matter. It's not like (1) the EU is asking to be allowed to install arbitrary programs on root servers or (2) it will start bombing non-compliant servers.
Worst case, EU residents (or at least residents using PCs sold in the EU) will only be able to access EU root servers, which will still index 100% of the internet. I'm not super worried.
In practice, though, I don't think it would matter. It's not like (1) the EU is asking to be allowed to install arbitrary programs on root servers or (2) it will start bombing non-compliant servers.
Worst case, EU residents (or at least residents using PCs sold in the EU) will only be able to access EU root servers, which will still index 100% of the internet. I'm not super worried.