Tyrconnell's expansion of the army by the creation of Catholic regiments was welcomed by Diarmuid Mac Carthaigh, as enabling the native Irish 'Tadhg' to be armed and to assert their dominance over 'John' the English Protestant.
The passage describes a situation where Tyrconnell's military actions are viewed favorably by Diarmuid Mac Carthaigh. This is because it allows for the empowerment of the native Irish, who are referred to as "Tadhg," and their ability to assert dominance over the English Protestants, who are called "John."