The Bayesian example given in the Wikipedia article looks like it works best with interval level data. Not sure it would work as well with ordinal data, because ordinals don't suffer to the same degree from outliers.
The second example also isn't ordinal data—it's just nominal "liked" vs "didn't like."
Both examples are interesting, but don't necessarily get at the problem with ordinal data introduced by the article.
It seems to me that the Bayesian average is superior, because it considers the value relative to other items.