None of your criticisms from wikipedia pertain to this publication. The paragraph is essentially making the argument that a randomized, double blind (DB), placebo controlled (PC) clinical trial (RCT) is unlikely to show that curcurmin is effective. yet, the published article is exactly that, and shows a statistically measurable impact on a clinically meaningful endpoint: a direct refutation of the paragraph.
the fact the "interference properties" and being an "unstable, reactive, non-bioavailable compound" is subsumed by the study design.
claims to have studied a bioavailable form of curcumin
This is not really relevant to the claim or conclusions. could it be that the bioavailability matters? maybe. could it be that curcurmin is a trick molecule to study? yes. but come what may, this is direct evidence (not proof) of a cause-effect relationship between this treatment and the outcome.
the only thing this effects is the chance that other forms of curcurmin will be comparable (and it might have consequences for regulatory status by the FDA).
The study also notes its sample was small
This is a very weak criticism when the study is
positive (i.e. shows an effect). when the sample size (and statistical power) of the study is small, you need a BIG EFFECT SIZE to be positive. The fact that the trial was positive actually means that it's more likely to be clinically important, because a big effect size means it protects memory in a dramatic way. This is like penicillin: in the pre-antibiotic era, how many cases of pneumonia do you need to treat in order to be satisfied that penicillin is effective? Not bloody many, because the effect size is so dramatic. Likewise for parachutes. few are the therapies that fall into this category, but when you have an inkling that one does following a DB, PC, RCT, you better pay attention.
So does it need to be replicated? definitely. does the sponsorship matter? definitely; they could have cheated in some way. until then does it make sense to prescribe this to seniors, or encourage them to increase curcurmin in their diet? quite possibly, given the presumably low rate of adverse effects.
Bottom line: this study is not the end-all be-all of curcurmin and memory, but there is legitimate early evidence that the emperor has clothes.
edits: mainly spelling, formatting