Scottish and Irish did not exist as national identities in this period, although Ireland, being an island, existed as a geographical identity. Dal Riata was a Gaelic kingdom governed in Old Gaelic, the language from which modern Irish, Manx and Scottish Gaelic all descend. In the early part of its existence, Dal Riata included land in both the Antrim and Argyll areas.
Ireland, Man and much of Western Scotland formed a geo-cultural area largely ruled by the Gaels in the early and high Medieval periods. At times, parts of this area were also controlled by Picts (speakers of a Brythonic Celtic language) and Norse vikings. There were likely more than a hundred kingdoms in the area, with petty kings giving allegiance to higher kings, but there was never one unified high king. Culture and language were no guarantee of unity - Gaelic, Pictish, and Norse kingdoms formed alliances at times and fought at others, but so did Gaels fight Gaels, Picts fight Picts, etc. The whole idea of national identity didn’t exist yet.
Although political boundaries eventually solidified in such a way that parts of the Gaelic world were in Ireland and parts in Scotland, strong cultural ties persisted into the early modern period, with poets and bards travelling throughout the whole region and a shared high register of Gaelic used for writing. Versions of the same tales and legends were collected in both areas well into the 20th century.