Oh good, FlyingPig is here.
Is Imperator Scottorum Emperor of Ireland or Emperor of the Irish?
Of the Irish; '-orum' denotes genetive plural.
Imperator Scotiae would be 'Emperor of Ireland' although 'Imperator Hibernae' would have been more usual: 'Scottus' denoted the Gaelic race (I'm trying hard not to say 'nation') so 'Scotia' was 'the land where the Gaels live', which originally meant most of Ireland, but since it was an ethnic term its meaning shifted - it was held in the early Middle Ages that Scotland and Ireland were populated by the same ethnic group, and so Ireland remained 'Scotia Maior' (the nuance of the term is hard to translate, but it really means 'the main land of the Gaels') while Scotland became 'Scotia Minor' ('the lesser land of the Gaels'). However, by about the 11th Century, Scotland was by a long way the most significant of the Gaelic political entities, and so 'Scotia' became synonymous with 'Alba'; that is, Scotland: the Pope, of all people, formalised this in the 15th Century.
So, to be honest - definitely 'Emperor of the Irish' rather than 'Emperor of Ireland', but it really means anything between that, 'Emperor of the Hiberno-Scottish Gaels', and 'Emperor of the Scots' - which in itself meant 'Britain north of the Forth' for quite some time - depending on the time in which it was used. One can understand why they chose the Latin title.
EDIT: If it's being used in the 14th Century, strictly it ought to be 'the Scots', but one can imagine it being used anachronistically to appeal to Gaelic ethnic identity (again, not saying nationalism!) and therefore to mean 'Emperor of the Gaels'. What makes things more complicated is that in the 11th Century we had the High King of Ireland using the
Imperator Scottorum title to mean 'Emperor of the Irish People' rather than of the Island of Ireland, but the English consistently used 'Hibernia' in their own titles, so in the 16th Century they established the King of England as 'Rex Hiberniae'.