The Romantic era emphasized, in brief, the appeal of the natural--nature, shepherds, pastoral life, etc--over the sophisticated and urbane. The Romantic era also emphasized the common language and speech of common people. In addition, in the Romantic era, the spiritual and the emblematic (nature providing symbols for meaning in life) and subjective is valued over the practical and objective.
Shaw's Pygmalion actually emphasizes the opposite of these qualities. (1) The Flower Girl represents the natural country life and she is not considered worthy to speak to her social betters except in accord with strict laws governing street sellers' behavior. (2) Her language is the most common possible ("Wal, fewd dan y' de-ooty bawmz a mather should, eed now bettern to spawl a pore gel's flahrzn than ran awy athaht pyin"), and it is the transformation of her language that is the subject of the play's focus, and it is her common ways that are the first to go as she is scrubbed then clothed in Japanese silk. (3) No emblematic symbolic figures are found in her unspoiled country ways that enlighten the spiritual aspects of life and lead to enlightenment. (4) Higgins whole approach to everything is decidedly practical and objective, as is the study of linguistics itself.
From this it must be concluded that there are no discernible elements of Romantic era literary philosophy in Shaw's Pygmalion. Some elements celebrated by Romantics might be identifiable in the Roman tale of Pygmalion by Ovid upon which Shaw drew for his story (the sculptor Pygmalion was so entranced by the beauty of his sculpture of a woman that he sought Venus to enliven her so he could wed her). However, because Shaw bases his play on the then relatively new scientific study of linguistics and the Darwinian-derived triumph of nurture over nature in the experiment of turning Liza into a woman who greatly improves upon nature, it is difficult to suggest that Shaw meant to embody any Romantic era literary philosophy in Pygmalion.