ABET does accredit international programs.
Some international programs. They don't have nearly enough capacity to accredit every single international engineering program all over the world. I'm sure they have the major ones down, but there's plenty that are probably not which still teach engineering.
> Engineer is a licensed profession, like physician or lawyer.
The license only gives you the right to call yourself a Professional Engineer. Like I said before, unless it is illegal to call yourself an engineer without being a PEng and being licensed, then the "licensed profession" part of it really does not matter. A company can require you to be a PEng in order to receive an "engineer" title in your role, but there is still nothing, short of law that prevents you from using it yourself.
> like physician or lawyer.
And they're both different from engineer, because those licensed professions are actually legally enforced, whereas "engineer" is not legally enforced everywhere.
This all varies between states, but in general, if you for example started a software consulting firm called Vlad Engineering and the principals were not licensed, your local licensing board would likely have beef with you. If you were a software engineer at Vlad Consulting you would probably be okay.
The bottom line is that it's tricky to navigate, and so it was recommended at my school we avoid using engineering anywhere unless we had our PE license.