This is based on the show's use of the language, which is actually modern Welsh with some archaic vocabulary and grammar added to make it sound older. While this isn't truly "Old Welsh" (a language that died out centuries ago), it's a close approximation and adds to the mystical and ancient atmosphere of the show.
It's worth noting that the language isn't specifically defined in the source material, Arthurian legends, as those are primarily written in Middle English and Latin. The show's writers took creative liberty in choosing Welsh, likely due to its connection to Wales and the mythical origins of King Arthur.