GP explicitly stated a case where the US did the same. So for all intents and purposes the law does propagate 'magically' over the internet. Well, at least US law does.
IANAL, but I think if you have a business establishment in a country then yes it may propagate in some shape or form, but I don't know the details. For instance, it may depend on distinctions such as subsidiary vs branch office.
Facebook does have a business establishment within the EU. They are selling ads in Europe that are delivered to EU users. There is no way that Facebook can claim not to be a European company in some sense.
You'll see. They will come to some arrangement with the publishers and regulators. Facebook will not lose a quarter of its revenues and profits over this.
The problem is that not many have the clout of Facebook and Google to work out arrangements that won't kill them or fight the whole thing effectively.
Thankfully foreign laws don't magically propagate over the internet, even if a citizen of a country happens to point their web browser at your server.