Presumably 'the' Nemea, since they are mentioned in a row with the Actia, Isthmia, Pythia, Olympia.
The name on the source, I.Sinope 105, gives as the second name 'Eoutios', which might be a mistake for 'Eou<s>tios', i.e. Justius, as per Farrington (2012), 143 note 463. The dating is given by Farrington (2012), 143 note 464, based on a lack of reference to Hadrianic contests and reference to possibly the Athenian or Ephesian Olympics. The source gives many victories apart from the Isthmian. Cf. for the source apart from SEG 13.540 also the lemmata 14.776, 16.750, 19.664. - PK