What he is saying is that NI players qualify to play for NI by virtue of the British citizenship that makes up part of their dual nationality status. All persons born in NI have this dual nationality status no matter which passport they carry. Whilst that may be a mere legal technicality which bears little or no relation to the identity of the player(s) in question, it remains the basis upon which they are able play for NI.
Irish nationality, and Irish nationality alone, does not qualify a player to play for NI. Such a player only qualifies to play for the ROI.