It's a continuum from "impossible to do with all the time and energy of the universe and the most advanced computers we have" to "my commodity hardware can crack it in a few minutes".
The same goes for fears of quantum computing breaking current cryptography. It goes from effectively impossible to "yeah, we could break it with a few years of constant computation, which is plenty of time to switch to quantum resistant schemes".
Even if the paper is correct it seems to fall into the 'moving down the continuum' category.
If there were, for example, a way to glean a private key without factoring the modulus, I think we'd all agree that this amounts to "breaking" the system insofar as that it changes the applicability of the hardness assumption.
On the other hand, simply achieving a faster way to factor the modulus is, at best, part of a continuum as you say.
That's not how you treat broken cryptography. If your data is already collected and stored encrypted by a third party which still holds value after several years, you're already in bad shape.