Everything else is just enforcement.

If you sell medical devices (apparently even down to toothbrushes) in the USA, you have to follow FDA rules. If you sell children's toys in the EU, you've had to follow EU consumer regulations (e.g. CE mark) at least since the 90s. Going back to the 70s, if you sold a physical product in the US as a foreign company you had to follow local rules about maximum delivery times and minimum warranties. If you don't follow the rules, your shipments get blocked at customs, and any marketplaces (Amazon) selling your products get fines as well for not verifying you appropriately, so marketplaces will verify and ban your business too if you blatantly violate local rules (e.g. selling devices containing radios without FCC approval). If you're selling laptops at any scale, you need to follow the local rules for every country you ship to.

There'll certainly be cases everywhere where enforcement isn't perfect (if you contact a tiny vendor in China and they ship to you directly and you sign for & pay the customs yourself, in practice you'll get away with it, or you can always travel to a country to buy a product and carry it back personally) but in the general case local regs on physical product sales are not unusual or optional at all.

They don't have to do business in EU if they don't want to follow the rules.