Playwright

A playwright, also known as a dramatist, is a person who writes plays.

The term is not a variant spelling of "playwrite", but something quite distinct: the word wright is an archaic English term for a craftsman or builder (as in a wheelwright or cartwright). Hence the prefix and the suffix combine to indicate someone who has "wrought" words, themes, and other elements into a dramatic form - someone who crafts plays. The homophone with "write" is in this case entirely coincidental.