What do you exactly mean by the word 'classical'? Yes, J.M. Synge's play Riders to The Sea definitely has a lot of classical features in terms of its resemblances with the Greek tragic drama, especially that of Sophocles. Maurya does look like a reconfiguration of the Greek prototypical mother who stands out as an embodiment of love, care and affection.
Maurya's dark, brooding and almost prophetic presence has another classical element in it and that is the way in which she responds to the recurrent catastrophes in her family. She has resigned herself to her fate and has developed a strong sense of premonition. She expects the worst, and she is well prepared for it, as it were. This stoical philosophy in her character as well her choric function in the play is definitely classical.
Maurya as a mother can also be considered classical in the sense that in her final speech she does not remain a specific mother to her family but elevates herself to a kind of generic, mythical and universal motherhood, praying for the well-being of all the sons upon this wretched fateful earth, moaning for all their tragedies, suffering on behalf of all of them.