"script from which a motion picture is made," 1916, from screen (n.) in the cinematic sense + play (n.).
Entries linking to screenplay
screen n.
mid-14c., screne, "upright piece of furniture providing protection from heat of a fire, drafts, etc.," probably from a shortened (Anglo-French? compare Anglo-Latin screna) variant of Old North French escren, Old French escran "fire-screen, tester of a bed" (early 14c.). This is of uncertain origin, though probably from a Germanic source, perhaps from Middle Dutch scherm "screen, cover, shield," or Frankish *skrank "barrier," from Proto-Germanic *skirmjanan(source also of Old High German skirm, skerm "protection," Old Frisian skirma "protect, defend;" from PIE root *sker- (1) "to cut").
The sense of "anything interposed to conceal from view" is by c. 1600. The meaning "net-wire frame used in windows and doors" is recorded from 1859. Meaning "flat vertical surface for reception of projected images" is from 1810, originally in reference to magic lantern shows; later of movies. Transferred sense of "cinema world collectively" is attested from 1914; hence screen test "filmed test of performing abilities" (1918), etc.
The meaning "small fluorescent display on a TV set" is by 1946, extended to the display on a computer monitor by 1970, hence the monitor itself. The computer screen saver is attested by 1990. The meaning "window of an automobile" is by 1904. As a type of maneuver in sports, by 1934 (U.S. football, screen-pass). Screen printing recorded from 1918. Screen-door is from 1840. Screen-time "time spent watching a computer or television screen" is by 1999.
play n.
Middle English pleie, from Old English plega (West Saxon), plæga (Anglian) "quick motion; recreation, exercise, any brisk activity" (the latter sense preserved in swordplay -- Old English sweordplegan -- etc.), from or related to Old English plegan (see play (v.)).
By early Middle English it could mean variously, "a game, a martial sport, activity of children, joke or jesting, revelry, sexual indulgence." Of physical things, "rapid, brisk, or light movement," by 1620s.
Meaning "dramatic performance" is attested by early 14c., perhaps late Old English. Meaning "free or unimpeded movement, liberty and room for action," of mechanisms, etc., is from 1650s. The meaning "activity, operation" (1590s) is behind expressions such as in full play, come into play. The sporting sense of "the playing of a game" is attested from mid-15c.; that of "specific maneuver or attempt" is from 1868.
The U.S. slang meaning "attention, publicity" is by 1929. To be in play (of a hit ball, etc.) is from 1788. Play-by-play in reference to running commentary on a game is attested from 1927. Play on words "pun" is from 1798. Play-money is attested from 1705 as "money won in gambling," by 1920 as "pretend money."