I think you're missing the key point (and perhaps the article doesn't explain it clearly): if the nervous system is completely different from other animals, then that implies (maybe) that the nervous system did not just evolve once, and then branch from there, but evolved multiple times, each time slightly differently but with similar results.
This is called "convergent evolution," and is fairly common (though not necessarily common for big systems like the nervous system), but what it implies is that there is something fundamental about the structure of the nervous system that leads it to being evolved again and again, even if in slightly different versions.
Contrast that to other things that are evolved, let's say endoskeletons (bones). These seem fundamental to us, but (as far as I know) they only evolved once, and it would be perfectly reasonable to imagine a world where they never evolved, and all the animals had exoskeletons.
Indeed, if endoskeletons really only evolved once, then we might really have no reason to expect them in any alien species. But if something like the nervous system evolved multiple times, then we expect that to be a solution that evolution finds again and again.