Amusingly ICAO (the UN aviation standardizations organization) has specified the ID card format for Machine Readable (Official) Travel Documents. And the passport card conforms to those specifications. But the only use of it that they officially encourage countries to accept is the Crew Member Certificate.
In all other cases, acceptance would be based on agreements between the involved countries. In theory, any country could choose to accept any such document without an agreement, but they have little reason to do so, and it is not really compatible with paper visas. Furthermore, they should refuse it if there are unmatched conditions printed on the back of the card, like the passport cards have. The result is that they are of pretty limited use, and most countries that do use them will restrict them to specific scenarios where there are agreements in place.
In all other cases, acceptance would be based on agreements between the involved countries. In theory, any country could choose to accept any such document without an agreement, but they have little reason to do so, and it is not really compatible with paper visas. Furthermore, they should refuse it if there are unmatched conditions printed on the back of the card, like the passport cards have. The result is that they are of pretty limited use, and most countries that do use them will restrict them to specific scenarios where there are agreements in place.