Most games require multiple players. However, single-player games are unique in respect to the type of challenges a player faces. Unlike a game with multiple players competing with or against each other to reach the game's goal, a one-player game is a battle solely against an element of the environment (an artificial opponent), against one's own skills, against time, or against chance. Playing with a yo-yo or playing tennis against a wall is not generally recognized as playing a game due to the lack of any formidable opposition.
It is not valid to describe a computer game as single-player where the computer provides opposition. If the computer is merely record-keeping, then the game may be validly single-player.
Many games described as "single-player" may be termed actually puzzles or recreations.