"writer or adapter of plays for the stage," 1680s (Ben Jonson used it 1610s as a mock-name), from play (n.) + wright (n.).
Old English wryhta, wrihta (Northumbrian wyrchta, Kentish werhta) "worker," variant of earlier wyhrta "maker," from wyrcan "to work" (see work (v.)). Now usually in combinations (wheelwright, playwright, etc.) or as a surname. A common West Germanic word; cognate with Old Saxon wurhito, Old Frisian wrichta, Old High German wurhto.
From: https://www.etymonline.com/search?q=playwright