For the (rare) headword verb prokateu/xomai see generally LSJ s.v. The present entry on it belongs in the category of Suda entries which make claims about the syntactical usage of verbs -- in this instance, its governing of the genitive case (likewise in Syntacticum Laurentianum pi59.7-8) -- implicitly rather than explicitly. (Contrast e.g. pi 2458.)
That the Suda's pronoun appears to presuppose such praying for a person need not always apply: witness Josephus, Jewish War 2.141, prokateu/xetai d' o( i(ereu\s th=s trofh=s "the priest prays in advance over the meal" (about the Essenes).