Word game

game that is based on knowledge of the language

Word games and puzzles are generally engaged as a source of  entertainment, but they have been found to serve a very useful and progressive educational purpose as well. For instance, young children can find enjoyment playing modestly competitive games such as Hangman, while naturally developing important language skills like spelling. Solving crossword puzzles, which requires familiarity with a larger vocabulary, is a pastime that mature adults have long credited with keeping their minds sharp.
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Noun
1. any game involving the formation or alteration or discovery of words
(hypernym) parlor game, parlour game
(hyponym) anagrams