Archaic or highly literary term for a medical doctor. In modern Japanese, 医者 or 医師 are the standard words.
He is researching physicians of the Edo period.
From 刀圭 (とうけい, 'medicine spoon') + 家 (か, 'person'). The term 刀圭 originally referred to a small spoon used for measuring medicine, later metonymically extended to mean a physician.