The headword is the present indicative middle, third person singular, of the late and rare verb periauti/zomai, I am busy about myself, brag; see generally LSJ s.v. It is evidently extracted from somewhere, perhaps Gregory of Nyssa, Letter 17.28 (the earliest attested instance). Other examples occur in e.g. the Histories of Theophylact Simocatta, and (favoured by Theodoridis) Cyril of Alexandria.
[1] The headword is identically glossed in Photius' Lexicon (pi641 Theodoridis) and the Synagoge; cf. Etymologicum Gudianum pi462.2, ps.-Zonaras 1542.3, Lexica Segueriana 337.16, and Hesychius. For the first of these glossing phrases see already under pi 1073; for a similar verb, see pi 1075.