No, they only have to satisfy the legal requirements of countries where they have established organizations. That's why GDPR was a game-changer: it made Europe-wide strong privacy regulations that were previously local to a few countries. France's CNIL has always been a farce, but at least on paper provided privacy rights... that Google was free to ignore because it was based in Ireland & such.

Of course as an Internet service you don't have to comply with every single national law there is. Would that even be possible? Of course, if a nation State believes you don't respect their laws, they are "free" to try and censor your website, as many do with The Pirate Bay, Sci Hub, etc.