Have you read the link you posted?
"The Minister for Justice, Equality and Defence, Mr. Alan Shatter, T.D., has signed Regulations transposing into Irish law an EU Directive requiring air carriers to provide advance passenger data to Irish Immigration authorities for the purposes of improving border control and combating illegal immigration.
The Regulations will apply to all inbound flights to Ireland from outside the EU and to all passengers on those flights."
It seems it is DSP staff who are doing the checking, not airline or airport staff. As I pointed out there is no way the airline of airport staff would be allowed to collect PPS numbers, or any other information not mandated by law, without breaching the GDPR. Given that plenty of airlines which are based outside the EU fly from Irish Airports there is no way that they would be allowed to collect sensitive personal data on EU citizens on behalf of an EU government. I'm not basing that on any conspiracy theory but rather the excellent personal data protection and privacy laws which are in place within the EU.