means A person who takes part in a game or sport, or — in slang — someone who skillfully manipulates romantic or social situations to their own advantage.

from From the Old English 'plega' (game, sport, brisk movement) via the verb 'pleg(i)an' (to exercise, frolic, perform), giving us 'play' and its agent-noun 'player.' For centuries it simply meant one who plays — at games, at music, on the stage (Shakespeare's 'all the world's a stage, and all the men and women merely players'). The romantic-operator sense is a much later slang extension, gaining traction in 20th-century American vernacular, where 'playing' someone shaded from playing a game into working an angle.