score:3
Schengen Annex II is the list of countries whose citizens enjoy visa-free access to the Schengen area for short-term visits. The passage you quote therefore means
People who enjoy visa-free access to the Schengen area by virtue of their nationality also enjoy visa-free access to Ireland, except for nationals of ...
The comparison is perhaps unhelpful to someone who simply wants to know whether they need a visa for Ireland, especially if that person is not familiar with Schengen policies.
Upvote:2
"Annex II" refers to Annex II of the EU regulation 539/2001
Specifically "Schengen Annex II nationalities" refers to citizens from one of the countries contained in this section of that document.