There is some confusion of terms in these recurring evolution debates. Evolution is used both for the idea that different species gradually develop from a common ancestor, and for the "mixing and mutations + natural selection" theory of how this development come about. If you, like the author of the first writeup, do not belive that the latter is primarily responsible for the former, you can certainly demonstrate it: just show the true cause.
Here I argue that the theory of natural selection is a valid one. The first argument in the original writeup seems to imply the second: A theory that makes predictions is falsifiable. It is true that we cannot use evolution to predict what kinds of animals will develop in a coral reef, but that is understandable because it is such a complex system. We cannot predict the weather a month from now either, but that's not because the Navier-Stokes equations are faulty.
In simpler contexts, evolutionary theory makes several predictions that are possible to verify:
- The emergence of pesticide-resistant insects, antibiotic-resitant bacteria, etc.
- That unrelated species in the same area will evolve towards similar forms (because that form is the "fittest"). Despite the eel/anglefish example, I think that is the case: colorful fishes in the tropic but not elsewhere, typical swimming configurations (e.g. "fish-like", like anglefish, sharks, and whales, and "snake-like" like watersnakes and eels).
- That different species develop in a "tree", whith diverse decendants developing from a common ancestor. (That is, the second sense of "evolution" above predicts the first). This can be verified by studying fossils, and by comparing unused portions of DNA of species belonging to the same large group.
At this point comes the counter-argument "but you are not really testing predictions, you are just supplying explanations after the fact. That's not science, and it's not the scientific method". To this I say that the scientific method of "hypothesize; derive predictions; test; repeat" is strongly idealised. In practise I do not think it is all uncommon that a theory is derived by "peeking" at the desired predictions.
The standard theory of natural selection has made predictions, some of which have only been possible to test with modern gene technology, and they have been confirmed. Competing theories like Lamarckianism also made predictions, and were falsified. If we are running out of ideas for new trials, and the burden of proof is starting to shift towards those who reject it, it might indeed make sense to stop calling Evolution a "theory". Thomas Kuhn used the term paradigm for such a theory.
Someone more bold might call it a fact.