US Passport Card for Identification (not customs) purposes

The purpose of American passport card confines entry into the United States by land or sea, confirmation of citizenship and identification. You can not expect all countries to accept it: especially those outside of Canada and Mexico and possibly some of the smaller countries near the USA for surface travel.

Even within the USA passport books and passport cards are reported as not accepted by some people, like bars and liquor shops.

In the rest of the world your experience will also differ, more by what the people checking are told to accept and reject than by authorities setting rules about accepting or rejecting USA passport cards.
I am pretty sure you will find tobacco shops, liquor shops and bars over the world which will accept your card, but the ones next to them may reject them, as not being on the official list.

I have successfully checked into hotels in Canada using my EU ID card, (basically the European equivalent of your US passport card,) and never got it rejected. But I always had my passport on hand as I keep it beneath my outer layer of clothes or safely in a bag, and at the ready, so I can have it out in a short time.

I do not expect your passport card to be accepted by border officials as it has no space for stamps. And as an official identification paper it only works as far as the check does not involve checking whether you are legal to be in the country at the time. (As that relies on stamps or visa.)

Even though you can enter many countries without a visa, you still have restrictions on how long you can stay. The current way of checking this is through the use of stamps in your passport.

So if police want to check your status, a passport card will not be enough, as it doesn’t have the entry stamp. For this reason, a passport card is usually not recognised by any foreign country outside of North America.

However, on a case by case basis, it really depends on the situation and why they are requesting ID. I would expect police to accept your passport card in some situations, but not others.

Note that in many countries, sadly, what you look like can have a strong bearing on whether you will be checked or not, as well as whether they will be inclined to accept alternative forms of ID. Expect more difficulty if you “look” like you are from Africa or Asia than if you look like the stereotypical American tourist with European origins.