Nobody has to worry about breaking Thai laws around defaming the King because Thailand isn’t a superpower with the ability to enforce its will beyond its borders.
Everyone has to be worried about breaking US law.
Not every country has this, so no, not "everyone has to be worried about breaking US law".
Regarding Thailand specifically, they have a principle of "double criminality", so people are only extraditable if what they're accused of is a crime both in Thailand and the country they're being extradited to. So maybe not the best example.
Besides, other countries have extradition treaties with other countries than the US too, even non-super power ones.