For example: you can't write to a file because of an I/O error, and when throwing that exception you find that you can't close the file either. What are you going to do about that other than possibly log the issue in the destructor? Wait and try again until it can be closed?
If you really must force Java semantics into it with chains of exception causes (as if anybody handled those gracefully, ever) then you can. Get the current exception and store a reference to the new one inside the first one. But I would much rather use exceptions as little as possible.
You need to read the article again because your assertion is patently false. You can throw and handle exceptions in destructors. What you cannot do is not catch those exceptions, because as per the standard uncaught exceptions will lead the application to be immediately terminated.
It's weird how you tried to frame a core design feature of the most successful programming language in the history of mankind as "useless".
Perhaps the explanation lies in how you tried to claim that exceptions had any place in "communicating non-fatal errors", not to mention that your scenario, handling non-fatal errors when destroying a resource, is fundamentally meaningless.
Perhaps you should take a step back and think whether it makes sense to extrapolate your mental models to languages you're not familiar with.