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1620s, "an athlete," agent noun from game (v.). Meaning "one devoted to playing video or computer games" is attested from 1999. Gamester is attested from 1590s but meant "prostitute" (cf. old slang the first game ever played "copulation"), later "a man fit and ready for anything, a player" (mid-17c.).
A brave and enterprising player, esp one who works with pain or against the odds: what is known in the business as a gamer, a guy who pitches with pain, who wants the ball/ When Jean Fuggett played for the Dallas Cowboys, his teammates called him a gamer
[1980s+ Baseball & football; probably fr game, ''brave, determined''; in the 1620s the word meant ''an athlete,'' and the current sense is conceivably though improbably a survival]