It is a type of nitpicking , imo, and just the title "The End of Theoretical Physics As We Know It " shows a person with a biased view on theoretical physics.
The abstract of the research you quote can be seen here and the accurate numbers have to do with the mass difference between proton and neutron,
The existence and stability of atoms rely on the fact that neutrons are more massive than protons. The measured mass difference is only 0.14% of the average of the two masses. A slightly smaller or larger value would have led to a dramatically different universe. Here, we show that this difference results from the competition between electromagnetic and mass isospin breaking effects. We performed lattice quantum-chromodynamics and quantum-electrodynamics computations with four nondegenerate Wilson fermion flavors and computed the neutron-proton mass-splitting with an accuracy of 300 kilo–electron volts, which is greater than 0 by 5 standard deviations. We also determine the splittings in the Σ, Ξ, D, and Ξcc isospin multiplets, exceeding in some cases the precision of experimental measurements.
unfortunately it is not an open link to the paper.
The calculations of the masses themselves have less accuracy and are works in progress in lattice QCD, here is a review.. My answer here discusses the situation.
So the statement " no one can calculate how they come together to make a proton" is placing very strict mathematical criteria for "calculate", in physics. If it is not a simple formula, it is of less value, denigrating the use of computers in theoretical physics calculations. In this frame of mind, lattice qcd calculations are not theoretical physics, because they use computers and not elbow grease to get at the numbers.
The quote of "shut up and calculate" was a saying long before supercomputers, and certainly needed elbow grease. Ihe statements: "The End of Theoretical Physics As We Know It " and " but no one can calculate how they come together to make a proton" can be paraphrased for novelists:
"The end of novel writing as we know it" and "no one can write longhand a manuscript for a novel". Confusing labor saving devices with creativity.