試合・しあい: a game: baseball, checkers, football, chess.
競争・きょうそう: a contest where the winner is judged by a third party: a marathon, two guys fighting over a lady, the best score on the test, the salesman who sold the most this month.
競技 :きょうぎ: games IN GENERAL. Like they don't say 'olympic games', they say 'olympic 競技’. or 'he really likes games' or ???
争う:あらそう:???
勝負:しょうぶ: ???
競う:きそう:???
闘う :???