Scientific Realism holds that in some sense scientific theories approximate the world, not just in what the experiments observe, but also in the content of their explanations (precisely, you gain knowledge not just about observables, but also non-observables: things that the theory requires to be true, but can't show). The article ascribes this view to Einstein, who presumably thought that there was a such thing as space-time, and it does actually curve under the influence of mass - despite only seeing things that are explained by the curvature, and not the curvature, or the space-time, itself.
The article then goes on to say that the anti-realist approach (dominated by not-undeserving practical concerns and application) focuses on computation: the mathematics is good so long as it gets the right answers in the end, and the end justifies the means. Therefore, it doesn't matter what contrivances must be dealt with in-between: if you get a better prediction, or can do a new exciting thing, then that was always the aim.
Thus, I read the article as advocating a stepping back from this view: it blames this focus on sheer mathematical sophistication as the route to truth as the source of profound disinterest in philosophy by physicists (it is important to note that I think that aeon is a philosophy newsletter!). Earlier and contemporary physicists (prominently, Einstein) had an interest in not just what their theories produced, but what they explained the world to be, and the article decries the modern lack of this.
I recommend the SEP article on scientific realism, which is dense but on a brief reading gives enough of the context to recognise the article. https://plato.stanford.edu/entries/scientific-realism/ (Although it is even more philosophically focused).
NB. I'm not a physicist or philosopher either, so grains of salt! My only self-endorsement is that I spent the last year reading a bit of philosophy, so perhaps I can be at least a stepping-stone to better resource.