If two unrelated proteins recognize the same binding interface, will they use similar patterns of residues or atoms to stabilize the interaction? The author looked for such patterns but did not find any -- the paper is thus about a negative result. However, this result very much depends on how we define similarity. The author's method fails an important test, namely to find similarities in cases of obvious structural mimicry (see my comment in the text).

To make a few guesses, the search for similar atoms in similar positions may be complicated by several issues: (1) flexibility and structure adaptations in the interface easily move residues and atoms by several Å. (2) rigid-body structure superpositioning tends to fit the core of a protein better than it's periphery. Fitting on the whole protein A may lead to errors in the position of B/C that are of similar order as the atom position cutoff.

Moreover, there are reports of structural motifs that are recurring across unrelated protein / peptide interfaces. E.g:
Protein-peptide interactions adopt the same structural motifs as monomeric protein folds. 2009, Structure
PMID: 19679090
(disclaimer: written by colleagues of mine).

So, in my opinion, the question addressed here is important but the results are not conclusive.