Eh, that's a highly uncharitable statement. Frameworks like "differential equations" or "group theory" or "quantum mechanics" also don't make falsifiable predictions (till you build a system-specific model which you can then compare against experiment) -- but that doesn't make them any less useful.
String theory in this unusual place between a physics model and a mathematical framework (that's what makes it so "fundamental"), and we are still in the process of figuring out how to construct predictive physical models using this framework. But OTOH it's been enormously useful in helping us theoretically probe and understand structural properties of quantum field theories, the implications of special symmetries, the geometry of manifolds, etc.
QM started as theory to explain otherwise unexplainable phenomenon, but explicitly provided things that could be falsified (aka tested), was immediately tested, and did indeed usefully describe otherwise unexplainable phenomenon before they were ever put forth seriously in any consistent way.
Algebra, group theory, etc. as pure math have proofs, but are definitely not (and never held out as) a physics theory.
Conflating the two is not appropriate. And saying string theory is a useful physics model while there is no way to test if anything unique it posits are true or not, may be useful mathematically - but means it’s not a physics model. Period.
That people spend so much time wedging everything into it to try to make it a useful model when it is unfalsifiable (and no one seems to have any idea how it would even BE falsifiable) is exactly the type of crisis the article is discussing.
Lots of careers built in a direction they can’t be proven wrong.
What the comment you are replying to said was that it is a mathematical formalism and not a physical model, and that they are still working to construct a physical model. So, it is not a physical theory, but the only people trained in it were first trained as physicists, and are employed by physics departments, and everything in it is constrained to fit in a physical theory.
The situation is far from ideal; there is no other plausible candidate for a physical theory compatible with gravitation and quantum field theory. But at the same time, we have literally no means to measure any case where they interact meaningfully. We can measure a fountain of cold neutrons falling in a gravitational field, but only the extremely weak field we are in. So, while it is a problem that nobody can devise a test for a physical string theory, nobody can devise a test for any other theory that would seek to fill the role.
String theory in this unusual place between a physics model and a mathematical framework (that's what makes it so "fundamental"), and we are still in the process of figuring out how to construct predictive physical models using this framework. But OTOH it's been enormously useful in helping us theoretically probe and understand structural properties of quantum field theories, the implications of special symmetries, the geometry of manifolds, etc.