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To study tongues from the Pleistocene, the period between 1.8 million and 10,000 years ago, Michael Dunn and his colleagues at the Max Planck Institute for Psycholinguistics developed a computer program that analyzes language based on how words relate to one another.

A computer program...that seals it.

Betwixt 1.8 million and 10,000 year ago...that nails it down.

Psycholinguistics...correction, pycho linguists.

Nothing can be definitively known about the sound of Attic Greek (500-300 B.C.), a mere 2500 years ago for which we have both literary and introspective evidence, and we're to believe that an automated method will reveal what we can already guess--languages can have structural similarities because we, as humans, have a inherent capacity for language, independent of their vocabularies. Further, we were told languages evolve from highly inflected to word order languages, and experts are WAG'ing that this process oscilates between some speculated extremes.

This is not science. But such often appears in "Science" magazine.

Why exactly is this not science?

A computer program...that seals it.
The same analysis could be done by hand, it would simply take a lot longer.

Betwixt 1.8 million and 10,000 year ago...that nails it down.
Scientists study events that happened long ago constantly in science.

Nothing can be definitively known about the sound of Attic Greek
Which has absolutely nothing to do with the study in question. There is no way to reproduce the sounds of a language, because the sounds didn't survive. However, the structure of a language can survive, which is why we still have people "speaking" Attic Greek even though the pronunciation is probably quite different.

The scientists used a new, experimental method to see whether they got the same results as using the old, tested method and it worked. After the successful test, they published their findings and asked other linguists to test the new method on the languages they were studying. More experimentation will show how much the theory is worth.

That's science.

Frequently the most critical differences between one language and another is not found in the grammatical structure or the vocabulary ~ instead, it is in the timing in the flow of the sounds and whether or not entire phrases and sentences have been reduced to rapidly spoken single words.

Analysis of that side of linguistic differences probably does look like "psycho linguistics" to someone who doesn't have an ear for it!

Methinks you're reading this wrong. They are not necessarily looking for structure or syntax of the ancient languages as much as they are looking to trace families of languages back farther than 10k years. For instance, using these methods, it might be possible to determine when one family diverged from another and from which geographical region both originated.