This is what is known as a slip jig, that is, a jig in 9/8 time. A slip jig has three beats to the bar, unlike the two beats of a regular (properly, double) jig. Hardiman the Fiddler is also in what is known as the mixolydian mode. The mixolydian is very similar to the major key, but it has one note (the 7th) that is flattened, giving it a distinctively powerful sound.
The tune is likely named after James Hardiman (1782–1855), a native of Galway. Hardiman wrote on various topics concerning Irish history and culture – not always well received. Inter alia he wrote Irish Minstrelsy in 1831. Whether he played the fiddle I do not know, but given his interest in Irish music, it is not inconceivable. Towards the end of his life Hardiman became the first librarian of the National University of Ireland, Galway, Library, which is now known as The James Hardiman Library.