Sounds good but is that true? A single unreplicated paper could be science couldn't it? Science is a framework within which there are many things, including theories, mistakes, false negatives, replication failures, etc... Science progresses due to quantity more than quality, it is brute force in some sense that way, but it is more a journey than a destination. You "do" science moreso than you "have" science.
A single brick on the ground, all by itself, is not a wall.
But if you take a lot of bricks and arrange them appropriately, then every single one of those bricks is wall.
In other words, just like the article points out down in the "dos" section, it depends on how you're treating that single unreplicated paper. Are you cherry-picking it, looking at it in isolation, and treating it as if it were definitive all by itself? Or are you considering it within a broader context of prior and related work, and thinking carefully about the strengths, limitations, and possible lacunae of the work it represents?
Only scientists care about doing science. Most people are not scientists. Even scientists are not scientists in every field. We as the genereral population (including scientists in a different field) however care about science because of the results. The results of science is modern health care, engineering (bridges that don't collapse...), and many other such things that we get because we "have" science.
I think you and the OP are agreeing with each other. The issue with a "single unreplicated paper" is exactly the issue you bring up with science as a journey. It's possible that this paper has found a genuine finding or that it is nonsense (people can find isolated published papers supporting almost anything they want even if they don't reflect the scientific consensus), but if no other researchers are even bothering to replicate the findings in it it hasn't joined the journey.