It’s hard to pin down a set of characteristics that is common to all games, because games can vary so broadly in form. Think about the differences in play between and even within these categories of games:
Card games: poker, blackjack, Hearts, solitaire, Killer Bunnies, Yu-Gi-Oh!, Magic: The Gathering
Board games: chess, checkers, backgammon, Clue, Scrabble, Pictionary, Trivial Pursuit, Twister, tic-tac-toe
Puzzles: crosswords, sudoku, Jumble, mazes, matchstick puzzles
Gambling: slot machines, roulette, craps, horse racing, state lotteries, office football pools
Sports: baseball, boxing, triathlon, ice hockey, Olympic ballroom dancing
Backyard games: tag, hide-and-seek, ...