But as you can see from the FIFA document, FIFA rely on passports as evidence of nationality. I think it's therefore safe to assume that when FIFA use the term "nationality", they're referring to citizenship.
That's simply not the case. The FIFA document asks for passports as evidence of nationality. Having a mother or grandparents of a certain nationality isn't evidence of nationality.
But he's not an Irish national from birth in law, so the Department of Foreign Affairs would be unable to supply such confirmation. He only became an Irish national in law upon the date of his birth being registered on the Foreign Births Register.
But they do ask for passports, because it is about citizenship. The section you've quoted in relation to documentary evidence from a governmental authority isn't to prove citizenship. A passport (or other ID) is required to prove that and it is dealt with in a separate section of that document. The section you've quoted relates to documentary confirmation of
when the player became an Irish citizen or national.
The document states that the FAI must send to FIFA "[a] recently issued statement dated and signed by the player in which he confirms that he understands the impact of such a change and that he is aware that such a change, if granted, is of a definite nature and irreversible". This implies that is a switch is not granted, then the player has not used up his option to switch once.
He can still switch to Sweden. And hasn't his request to switch to Ireland already been rejected? Is that not how this issue arose? The player himself
spoke of a complication with the paperwork. As I understand it, the FAI are now liaising with FIFA to try and find a way around their rejection of his request.
According to the Irish Department of Foreign Affairs, she's an Irish national under Irish law. As geysir quoted the Department above: "Being an Irish citizen means that you are formally recognised as a national of Ireland and a citizen of the European Union."